MATH-1150-LN01&LN04&WBP02

Handouts are stored on this page in DjVu format; see the DjVu help if you have trouble reading these files. (They're avaialable in PDF on Canvas; see the link for your section immediately below.) See also the SCC syllabus (DjVu), the SCC Course Statements and the SCC Student Technical Support Resources (DjVu).

Course administration

For Section LN01

• Canvas page (where you must log in).
• My course policies (DjVu).
• Class hours: Mondays, Wednesdays, and Fridays from 9:00 to 9:50 in room U103.
• Final exam time: December 10 Wednesday from 9:00 to 10:40 in room U103 (or by appointment).

For Section LN04

• Canvas page (where you must log in).
• My course policies (DjVu).
• Class hours: Tuesdays and Thursdays from 11:00 to 12:20 in room U5.
• Final exam time: December 11 Thursday from 11:00 to 12:40 in room U5 (or by appointment).

For Section WBP02

• Canvas page (where you must log in).
• My course policies (DjVu).
• Class hours: Online only.
• Final exam time: By appointment only.

Contact information

• Name: Toby Bartels, PhD.
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Office hours: Weekdays from 10:00 to 10:50 (or by appointment) in room U9C (or over Zoom meeting 610-024-2876).

Readings

All of the dates below (and most of the numbering) are wrong for Section LN04, although the assignments (readings and exercises) are correct. (This is to avoid duplicating everything. The numbering and dates are correct on Canvas.)

Try to read this introduction before the first day of class:

• Objectives:
  • Understand what to expect from this course;
  • Know how to submit assignments.
• Reading:
  • The course policy document for your section above;
  • My online introduction.
• Reading homework due on August 18 Monday or ASAP thereafter in Section WBP02 (submit this on Canvas):
  1. If you need to submit an assignment that you've written out by hand (especially a graph, a table, or a complicated mathematical expression), then how will you send me a picture of that?
  2. How will you get the final exam proctored? (Lincoln Testing Center, ProctorU, etc).
  You can change your mind about these later! (But let me know if you change your mind about #2.)
• Problem Set from the textbook due on August 20 Wednesday or ASAP thereafter (submit this through MyLab): O.1.1, O.1.2, O.1.3, O.1.4, O.1.5, O.1.6, O.1.7, O.1.8, O.1.10, O.1.12.

Graphs and functions

1. General review: A review of algebra that you should already know.
   • Objectives:
     • Review the real and complex number systems;
     • Review exponentiation with rational exponents;
     • Review evaluating and simplifying algebraic expressions;
     • Review testing and solving algebraic equations;
     • Solve and graph linear inequalities in one variable.
   • Reading: Skim Chapter R (except Section R.6) and Chapter 1 (except Section 1.6) from the textbook, and review anything that you don't remember well.
   • Reading homework due on August 20 Wednesday (submit this in class or on Canvas):
     1. Which of the following are equations? (Say Yes or No for each.)
        1. 2x + y;
        2. 2x + y = 0;
        3. z = 2x + y.
     2. You probably don't know how to solve the equation x⁵ + 2x = 1, but show what numerical calculation you make to check whether x = 2 is a solution.
     3. Write the set {x | x < 3} in interval notation and draw a graph of the set.
     4. Suppose that ax² + bx + c = 0 but a ≠ 0; write down a formula for x.
   • Problem set from the textbook due on August 22 Friday (submit this through MyLab): 1.1.27, 1.1.39, 1.2.23, 1.2.49, 1.3.63, 1.5.71, 1.5.75, 1.7.33, 1.7.47.
2. Graphing review: Geometry in the coordinate plane.
   • Objectives:
     • Review the rectangular coordinate system;
     • Graph equations with tables of values;
     • Find intercepts of graphs;
     • Test equations and graphs for symmetry.
   • Reading:
     • Review Section 2.1 through "Rectangular Coordinates" (pages 150&151) from the textbook;
     • Read Section 2.2 (pages 158–165) from the textbook (this should be review at the start but might be new material by the end);
     • My online notes on symmetry and intercepts.
   • Reading homework due on August 22 Friday (submit this in class or on Canvas):
     1. Fill in the blanks with vocabulary words: The two number lines that mark the coordinates in a rectangular coordinate system are the coordinate _____, and the point where they intersect is the _____.
     2. Fill in the blanks with a vocabulary word: Given a graph in a coordinate plane, a point on the graph that lies on at least one coordinate axis is a(n) _____ of that graph.
     3. Fill in the blank: If for each point (x, y) on a graph, the point (−x, y) is also on the graph, then the graph is symmetric with respect to the _____.
   • Problem set from the textbook due on August 25 Monday (submit this through MyLab): 2.1.15, 2.1.17, 2.2.13, 2.2.17, 2.2.23, 2.2.29, 2.2.31, 2.2.33, 2.2.35, 2.2.41, 2.2.43, 2.2.45, 2.2.47, 2.2.53, 2.2.55, 2.2.61, 2.2.67, 2.2.71, 2.2.77.
3. Graphing lines: Lines in the coordinate plane.
   • Objectives:
     • Calculate the run, rise, and slope from one point to another;
     • Calculate the distance and midpoint between two points;
     • Find an equation of a line given graphical information about it;
     • Find graphical properties of a line given an equation;
     • Handle vertical lines.
   • Reading:
     • The rest of Section 2.1 (pages 151–154) from the textbook;
     • My online notes on lines and line segments;
     • Section 2.3 through Objective 7 (pages 169–176) from the textbook.
   • Reading homework due on August 25 Monday (submit this in class or on Canvas):
     1. Fill in the blanks with algebraic expressions: The distance between the points (x₁, y₁) and (x₂, y₂) is _____, and the midpoint between them is (___, ___).
     2. Write an equation for the line in the (x, y)-plane with slope m and y-intercept (0, b).
     3. Fill in the blanks with words or numbers: The slope of a vertical line is _____, and the slope of a horizontal line is _____.
   • Problem set from the textbook due on August 27 Wednesday (submit this through MyLab): 2.1.19, 2.1.33, 2.1.39, 2.1.47, 2.3.2, 2.3.13, 2.3.15, 2.3.17, 2.3.19, 2.3.21, 2.3.23, 2.3.25, 2.3.27, 2.3.29, 2.3.31, 2.3.45, 2.3.53, 2.3.57, 2.3.63, 2.3.79, 2.3.85, 2.3.91, 2.3.93.
4. Linear equations: Parallel and perpendicular lines, and when two linear equations might be true at once.
   • Objectives:
     • Identify when two lines are parallel or perpendicular;
     • Find the slope of a line given a parallel or perpendicular line;
     • Test solutions of systems of equations;
     • Solve simple systems of linear equations by graphing.
   • Reading:
     • The rest of Section 2.3 (pages 176–179) from the textbook;
     • The introduction to Section 12.1 (pages 877–879) from the textbook.
   • Reading homework due on August 27 Wednesday (submit this in class or on Canvas):
     1. Fill in the blanks with numbers: Suppose that a line L has slope 2. The slope of any line parallel to L is ___, and the slope of any line perpendicular to L is ___.
     2. Answer Yes or No: Suppose that you have a system of equations and a point that might be a solution. If the point is a solution to one equation in the system but not a solution to another equation in the system, then is that point a solution to the system of equations?
   • Problem set from the textbook due on August 29 Friday (submit this through MyLab): 2.3.7, 2.3.8, 2.3.51, 2.3.67, 2.3.73, 2.3.75, 2.3.111, 2.3.113, 12.1.11, 12.1.13, 12.1.15, 12.1.17.
5. Systems of equations: Systems of two or three linear equations in the same number of variables.
   • Objectives:
     • Solve systems of linear equations in two or three variables;
     • Compare two methods for solving systems of linear equations;
     • Classify systems of linear equations (with the same number of equations as variables) as consistent or inconsistent, and dependent or independent.
   • Reading:
     • The rest of Section 12.1 (pages 880–887) from the textbook;
     • My online notes and video on systems of equations.
   • Reading homework due on August 29 Friday (submit this in class or on Canvas):
     1. Given a system of two equations in the two variables x and y, if the graphs of the two equations intersect at (and only at) the point (3, 5), then what is the solution of the system? (Give explicitly the value of x and the value of y.)
     2. Consider the system of equations consisting of x + 3y = 4 (equation 1) and 2x + 3y = 5 (equation 2).
        1. If I solve equation (1) for x to get x = 4 − 3y and apply this to equation (2) to get 2(4 − 3y) + 3y = 5 (and continue from there), then what method am I using to solve this system?
        2. If instead I multiply equation (1) by −2 to get −2x − 6y = −8 and combine this with equation (2) to get −3y = −3 (and continue from there), then what method am I using to solve this system?
   • Problem set from the textbook due on September 3 Wednesday (submit this through MyLab): 12.1.3, 12.1.4, 12.1.6, 12.1.19, 12.1.21, 12.1.27, 12.1.31, 12.1.45, 12.1.47, 12.1.65, 12.1.73.
6. Systems of inequalities: Systems of two linear inequalities in two variables.
   • Objectives:
     • Compare weak and strict inequalities;
     • Graph linear inequalities in two variables;
     • Graph systems of linear inequalities in two variables.
   • Reading: Section 12.7 (pages 951–956) from the textbook except Examples 3 and 8.
   • Reading homework due on September 3 Wednesday (submit this in class or on Canvas):
     1. Fill in the blank: If a system of equations or inequalities has no solutions, then the system is _____.
     2. Suppose you are graphing a contingent linear inequality in two variables.
        1. If the inequality is strict (with < or >), then should the boundary line be solid or dashed?
        2. If the inequality is weak (with ≤ or ≥), then should the boundary line be solid or dashed?
   • Problem set from the textbook due on September 5 Friday (submit this through MyLab): 12.7.13, 12.7.14, 12.7.15, 12.7.23, 12.7.25, 12.7.27, 12.7.29, 12.7.31.
7. Functions: The heart of the course.
   • Objectives:
     • Become familiar with the concept of a function between real numbers;
     • Evaluate a function using a formula for it;
     • Represent a function as a relation;
     • Determine whether an equation defines a function;
     • Identify the domain and range of a function;
     • Calculate the domain from a formula for a function;
     • Apply arithmetic operations to functions.
   • Reading:
     • Section 3.1 (pages 203–215) from the textbook;
     • My online notes on functions.
   • Reading homework due on September 5 Friday (submit this in class or on Canvas):
     1. Fill in the blank with a mathematical expression: If g(x) = 2x + 3 for all x, then g(___) = 2(5) + 3 = 13.
     2. Fill in the blank with an equation, inequality, or other statement: If a function f is thought of as a relation, then it's the relation {x, y | _____}.
     3. Fill in the blanks with vocabulary words: If f(3) = 5, then 3 belongs to the _____ of the function f, and 5 belongs to its _____.
     4. Fill in the blank with an arithmetic operation: If f(x) = 2x for all x, and g(x) = 3x for all x, then (f ___ g)(x) = 5x for all x.
   • Problem set from the textbook due on September 8 Monday (submit this through MyLab): 3.1.1, 3.1.2, 3.1.3, 3.1.10, 3.1.31, 3.1.33, 3.1.35, 3.1.37, 3.1.43, 3.1.49, 3.1.51, 3.1.53, 3.1.55, 3.1.59, 3.1.63, 3.1.71, 3.1.79, 3.1.81, 3.1.103, 3.1.117.
8. Graphs of functions: Functions can be thought of geometrically, as particular sorts of graphs in the coordinate plane.
   • Objectives:
     • Graph a function from a formula using a table of values;
     • Use the Vertical-Line Test to decide whether a graph is the graph of a function;
     • Evaluate a function using points on its graph;
     • Find the domain and range of a function from its graph.
   • Reading: Section 3.2 (pages 219–223) from the textbook.
   • Reading homework due on September 8 Monday (submit this in class or on Canvas):
     1. Fill in the blanks with mathematical expressions: If (2, 4) is a point on the graph of a function f, then f(___) = ___.
     2. Fill in the blank with a geometric word: The graph of a relation is the graph of a function if and only if every _____ line goes through the graph at most once.
     3. Which of these is true, and which of these is false?
        1. The graph of a function can have any number of x-intercepts;
        2. The graph of a function can have any number of y-intercepts.
   • Problem set from the textbook due on September 10 Wednesday (submit this through MyLab): 3.2.7, 3.2.9, 3.2.11, 3.2.13, 3.2.16, 3.2.17, 3.2.19, 3.2.21, 3.2.27, 3.2.29, 3.2.31, 3.2.33, 3.2.39, 3.2.43, 3.2.47.

Properties and types of functions

9. Properties of functions: Thinking of a function as a thing in its own right, it can have various properties and characteristics.
   • Objectives:
     • Use a formula to determine whether a function is even or odd;
     • Use a graph to determine whether a function is even or odd;
     • Use a formula to find the intercepts of the graph of a function.
   • Reading:
     • Section 3.3 through Objective 2 (pages 229–231) from the textbook;
     • My online notes on properties of functions.
   • Reading homework due on September 10 Wednesday (submit this in class or on Canvas): Fill in the blanks with vocabulary words:
     1. Suppose that f is a function and, whenever f(x) exists, then f(−x) also exists and equals f(x). Then f is _____.
     2. If c is a number and f is a function, and if f(c) = 0, then c is a(n) _____ of f. (This one is not in the textbook until Chapter 5, but it is in my notes for this lesson.)
   • Problem set from the textbook due on September 12 Friday (submit this through MyLab): 3.3.3, 3.3.5, 3.3.37, 3.3.39, 3.3.41, 3.3.43, 3.3.45.
10. Rates of change: Properties of functions related to slopes of lines.
    • Objectives:
      • Calculate the rate of change of a function on an interval;
      • Determine from a graph where a function is increasing, decreasing, or constant;
      • Find local maxima and minima from a graph;
      • Find absolute maxima and minima from a graph.
    • Reading: The rest of Section 3.3 (pages 231–237) from the textbook.
    • Reading homework due on September 17 Wednesday (submit this in class or on Canvas): Fill in the blanks with vocabulary words:
      1. Suppose that a function f is defined on (at least) a nontrivial interval I and that, whenever a ∈ I and b ∈ I, if a < b, then f(a) < f(b). Then f is (strictly) _____ on I.
      2. Suppose that f(x) = M for at least one value of x, and f(x) ≤ M for every value of x. Then M is the absolute _____ of f.
    • Problem set from the textbook due on September 19 Friday (submit this through MyLab): 3.3.2, 3.3.13, 3.3.15, 3.3.17, 3.3.19, 3.3.21, 3.3.23, 3.3.25, 3.3.27, 3.3.29, 3.3.31, 3.3.49, 3.3.51.
11. Word problems with functions: Using functions to solve systems of equations with too many variables.
    • Objectives:
      • Set up algebraic equations to describe word problems;
      • Solve systems of equations with too few variables to express quantities as a function of one of the variables.
    • Reading:
      • Section 3.6 (pages 267–269) from the textbook;
      • My online notes and video on functions in word problems.
    • Reading homework due on September 19 Friday (submit this in class or on Canvas): Suppose that you have a problem with three quantities, A, B, and C; and suppose that you have two equations, equation (1) involving A and B, and equation (2) involving B and C. If you wish to find A as a function of C, then which equation should you solve first, and which variable should you solve it for? (Although there is a single best answer in my opinion, there is more than one answer that will progress the solution, and I'll accept either of them.)
    • Problem set from the textbook due on September 22 Monday (submit this through MyLab): 3.6.5, 3.6.13, 3.6.15, 3.6.21, 3.6.23.
12. Linear functions: A particularly simple kind of function with a consistent rate of change.
    • Objectives:
      • Identify a linear function from a formula or a graph;
      • Determine if a table of values could come from a linear function;
      • Graph linear functions;
      • Find the rate of change and initial value of a linear function;
      • Solve word problems using linear functions;
      • Compare linear functions using their graphs.
    • Reading: Section 4.1 (pages 281–287) from the textbook.
    • Reading homework due on September 22 Monday (submit this in class or on Canvas):
      1. Suppose that y is linear function of x. If the rate of change of the function is m and the initial value of the function is b, then write an equation relating x and y.
      2. Suppose that f is a linear function. If you know f(x₁) and f(x₂) for two distinct real numbers x₁ and x₂, then give a formula for the slope of the graph of f using x₁, x₂, f(x₁), and/or f(x₂).
    • Problem set from the textbook due on September 24 Wednesday (submit this through MyLab): 4.1.2, 4.1.13, 4.1.15, 4.1.17, 4.1.19, 4.1.21, 4.1.23, 4.1.25, 4.1.27, 4.1.37, 4.1.43, 4.1.45, 4.1.47, 4.1.49.
13. The library of functions: More simple examples that you should become familiar with.
    • Objectives:
      • Become familiar with the identity function;
      • Become familiar with the square function;
      • Become familiar with the cube function;
      • Become familiar with the principal square-root function;
      • Become familiar with the cube-root function;
      • Become familiar with the reciprocal function;
      • Become familiar with the absolute-value function.
    • Reading: Section 3.4 Objective 1 (pages 242–246) from the textbook.
    • Reading homework due on September 24 Wednesday (submit this in class or on Canvas):
      1. In the _____ function, the output is always defined and equal to the input.
      2. If you reflect the graph of the cube function across the diagonal line where y = x, then you get the graph of the _____ function.
    • Problem set from the textbook due on September 26 Friday (submit this through MyLab): 3.4.9, 3.4.11, 3.4.13, 3.4.14, 3.4.15, 3.4.16, 3.4.17, 3.4.18, 3.4.19, 3.4.20, 3.4.21, 3.4.22, 3.4.23, 3.4.24, 3.4.25, 3.4.26.
14. Piecewise-defined functions: One way to combine simple functions to make more complicated ones.
    • Objectives:
      • Define a partially-defined function with a formula and a condition;
      • Define a piecewise-defined function with multiple formulas and conditions;
      • Evaluate a piecewise-defined function;
      • Graph a piecewise-defined function;
      • Find inputs of a piecewise-defined function.
    • Reading:
      • My online notes and video on partially-defined functions;
      • The rest of Section 3.4 (pages 247–249) from the textbook.
    • Reading homework due on September 26 Friday (submit this in class or on Canvas): Fill in the blanks with vocabulary words:
      1. A _____-defined function is defined by a formula together with a condition restricting its inputs;
      2. A _____-defined function is defined by more than one formula, each with a condition restricting its inputs.
    • Problem set from the textbook due on September 29 Monday (submit this through MyLab): 3.4.10, 3.4.27, 3.4.29, 3.4.31, 3.4.33, 3.4.35, 3.4.43, 3.4.45, 3.4.51.
15. Composite functions: Taking the output of one function and using it as the input to another.
    • Objectives:
      • Evaluate a composite function;
      • Find a formula for a composite function;
      • Find the domain of a composite function.
    • Reading:
      • Section 6.1 (pages 415–419) from the textbook;
      • My online notes on composite functions.
    • Reading homework due on September 29 Monday (submit this in class or on Canvas):
      1. Fill in the blanks with a vocabulary word and a mathematical expression: If f and g are functions, then their _____ function, denoted f ∘ g, is defined by (f ∘ g)(x) = _____.
      2. Fill in the blanks with mathematical expressions: A number x is in the domain of f ∘ g if and only if ___ belongs to the domain of g and ___ belongs to the domain of f.
    • Problem set from the textbook due on October 1 Wednesday (submit this through MyLab): 6.1.2, 6.1.9, 6.1.11, 6.1.15, 6.1.19, 6.1.25, 6.1.27, 6.1.29, 6.1.33, 6.1.55.
16. Inverse functions: Can we run a function backwards?
    • Objectives:
      • Determine from its graph whether a function is one-to-one;
      • Find a formula for the inverse of a one-to-one function;
      • Graph the inverse of a one-to-one function;
      • Find the range of a one-to-one function.
    • Reading:
      • Section 6.2 (pages 423–430) from the textbook;
      • My online notes on inverse functions.
    • Reading homework due on October 1 Wednesday (submit this in class or on Canvas):
      1. Fill in the blank with a geometric word: A function is one-to-one if and only if every _____ line goes through its graph at most once.
      2. Fill in the blank with a vocabulary word: If f is a one-to-one function, then its _____ function, denoted f⁻¹, exists.
      3. Fill in the blank with an ordered pair: If f is one-to-one and (2, −3) is on the graph of f, then ___ is on the graph of f⁻¹.
      4. Fill in the blanks with vocabulary words: If f is one-to-one, then the domain of f⁻¹ is the _____ of f, and the range of f⁻¹ is the _____ of f.
    • Problem set from the textbook due on October 3 Friday (submit this through MyLab): 6.2.4, 6.2.5, 6.2.7, 6.2.8, 6.2.9, 6.2.12, 6.2.21, 6.2.23, 6.2.25, 6.2.35, 6.2.37, 6.2.39, 6.2.43, 6.2.45, 6.2.49, 6.2.51, 6.2.53, 6.2.63, 6.2.65, 6.2.67, 6.2.69, 6.2.83, 6.2.85, 6.2.87, 6.2.95.
17. Linear coordinate transformations: We can easily graph composites with linear functions.
    • Objectives:
      • Graph an outside translation of a function by shifting it up or down;
      • Graph an outside scaling of a function by stretching or compressing it up and down;
      • Graph an outside reflection of a function by flipping it up and down;
      • Graph an inside translation of a function by shifting it left or right;
      • Graph an inside scaling of a function by stretching or compressing it left and right;
      • Graph an inside reflection of a function by flipping it left and right;
      • Graph a function with a combination of these transformations.
    • Reading:
      • Section 3.5 (pages 254–263) from the textbook;
      • My online notes on linear coordinate transformations.
    • Reading homework due on October 3 Friday (submit this in class or on Canvas): Assume that the axes are oriented in the usual way (positive x-axis to the right, then positive y-axis upwards).
      1. Fill in the blank with a direction: To change the graph of y = f(x) into the graph of y = f(x − 1), shift the graph to the ___ by 1 unit;
      2. To change the graph of y = f(x) into the graph of y = −f(x), do you reflect the graph left and right or up and down?
      3. To change the graph of y = f(x) into the graph of y = f(2x), do you compress or stretch the graph left and right?
    • Problem set from the textbook due on October 6 Monday (submit this through MyLab): 3.5.5, 3.5.6, 3.5.7, 3.5.9, 3.5.11, 3.5.13, 3.5.15, 3.5.17, 3.5.19, 3.5.21, 3.5.23, 3.5.25, 3.5.29, 3.5.30, 3.5.33, 3.5.35, 3.5.37, 3.5.41, 3.5.43, 3.5.45, 3.5.47, 3.5.53, 3.5.61, 3.5.63, 3.5.73, 3.5.89.

Exponential and logarithmic functions

18. Exponential functions: Can we make sense of raising to the power of an irrational exponent, and what kind of function does this give us?
    • Objectives:
      • Define raising a positive number to the power of an irrational number;
      • Use a scientific calculator to raise numbers to powers;
      • Identify generalized exponential functions;
      • Graph generalized exponential functions;
      • Find properties of generalized exponential functions.
    • Reading:
      • Section 6.3 (pages 435–446) from the textbook;
      • My online notes on exponential functions.
    • Reading homework due on October 6 Monday (submit this in class or on Canvas): Assume that b > 0, and let f(x) be Cb^x for all x. Answer the following questions using b and/or C, and simplify them as much as possible.
      1. What is f(x + 1)/‍f(x)?
      2. What are f(−1), f(0), and f(1)?
    • Problem set from the textbook due on October 8 Wednesday (submit this through MyLab): 6.3.1, 6.3.17, 6.3.18, 6.3.23, 6.3.25, 6.3.27, 6.3.29, 6.3.31, 6.3.33, 6.3.35, 6.3.37, 6.3.39, 6.3.41, 6.3.43, 6.3.45, 6.3.47, 6.3.49, 6.3.53, 6.3.55, 6.3.59, 6.3.61, 6.3.63, 6.3.67, 6.3.69, 6.3.73, 6.3.75, 6.3.78, 6.3.79, 6.3.81, 6.3.85, 6.3.87, 6.3.93, 6.3.95.
19. Logarithmic functions: We can reverse exponentiation to get roots, but another way of reversing it gives us logarithms instead.
    • Objectives:
      • Define real-valued logarithms of positive numbers;
      • Define common and natural logarithms;
      • Calculate rational-valued logarithms by solving an exponential equation;
      • Graph logarithmic functions;
      • Find properties of logarithmic functions.
    • Reading:
      • Section 6.4 through Objective 4 (pages 452–457) from the textbook;
      • My online notes on logarithmic functions.
    • Reading homework due on October 8 Wednesday (submit this in class or on Canvas): Suppose that b > 0 and b ≠ 1.
      1. Rewrite log_b M = r as an equation involving exponentiation.
      2. What are log_b b, log_b 1, and log_b (1/‍b)?
    • Problem set from the textbook due on October 10 Friday (submit this through MyLab): 6.4.13, 6.4.15, 6.4.17, 6.4.19, 6.4.21, 6.4.23, 6.4.25, 6.4.27, 6.4.29, 6.4.31, 6.4.33, 6.4.35, 6.4.37, 6.4.39, 6.4.41, 6.4.45, 6.4.53, 6.4.55, 6.4.57, 6.4.59, 6.4.67, 6.4.69, 6.4.71, 6.4.73, 6.4.75, 6.4.81, 6.4.85, 6.4.87.
20. Converting logarithms: Inverse functions involving logarithms, and how to get your calculator to find a logarithm when it doesn't have the right button.
    • Objectives:
      • Find inverse functions of linear coordinate transformations of exponential functions;
      • Find inverse functions of linear coordinate transformations of logarithmic functions;
      • Convert bases of logarithms;
      • Calculate logarithms using common or natural logarithms.
    • Reading:
      • Section 6.4 Objective 5 (pages 457–460) from the textbook;
      • Section 6.5 Objective 4 (pages 469–471) from the textbook.
    • Reading homework due on October 17 Friday (submit this in class or on Canvas): Assuming that b > 0, b ≠ 1, and u > 0, write log_b u in these two ways:
      1. Using only common logarithms (logarithms base 10);
      2. Using only natural logarithms (logarithms base e).
    • Problem set from the textbook due on October 20 Monday (submit this through MyLab): 6.4.91, 6.4.93, 6.4.95, 6.4.97, 6.4.99, 6.4.101, 6.4.103, 6.4.105, 6.4.107, 6.4.109, 6.4.111, 6.4.113, 6.4.121, 6.4.131, 6.4.133, 6.5.7, 6.5.11, 6.5.71, 6.5.73, 6.5.75, 6.5.78.
21. Logarithmic expressions: Working with logarithms in algebraic expressions.
    • Objectives:
      • Review properties of exponentiation;
      • Break down logarithmic expressions;
      • Combine logarithmic expressions;
      • Simplify logarithmic expressions by converting bases.
    • Reading:
      • Section 6.5 through Objective 3 (pages 465–469) from the textbook;
      • Section 6.5 Summary (page 471) from the textbook;
      • My online notes on laws of logarithms.
    • Reading homework due on October 20 Monday (submit this in class or on Canvas):
      1. Fill in the blank with a number: b⁰ = ___.
      2. Fill in the blank with an arithmetic operation: b^x−y = b^x ___ b^y.
      3. Fill in the exponent with an algebraic expression involving n: If n ≠ 0, then ⁿ√b = b^□.
      4. Fill in the blanks to break down these expressions using properties of logarithms. (Assume that b, u, and v are all positive and that b ≠ 1.)
         1. log_b (uv) = ___;
         2. log_b (u/‍v) = ___;
         3. log_b (u^x) = ___.
    • Problem set from the textbook due on October 22 Wednesday (submit this through MyLab): 6.5.13, 6.5.15, 6.5.17, 6.5.19, 6.5.21, 6.5.23, 6.5.25, 6.5.27, 6.5.37, 6.5.39, 6.5.41, 6.5.43, 6.5.45, 6.5.47, 6.5.49, 6.5.51, 6.5.53, 6.5.55, 6.5.57, 6.5.61, 6.5.63, 6.5.65, 6.5.67, 6.5.69, 6.5.87, 6.5.91, 6.5.97.
22. Logarithms and equations: How to solve an equation with logarithms in it, and how to use logarithms to solve other equations.
    • Objectives:
      • Solve exponential and logarithmic equations in which the variable appears only once;
      • Solve equations in which the variable appears inside several logarithms;
      • Solve equations in which the variable appears inside several exponents.
    • Reading: Section 6.6 through Objective 2 (pages 474–477) from the textbook.
    • Reading homework due on October 22 Wednesday (submit this in class or on Canvas): In solving which of the following equations would it be useful to have a step in which you take logarithms of both sides of the equation? (Say Yes or No for each one.)
      1. log₂ (x + 3) = 5;
      2. (x + 3)² = 5;
      3. 2^x+3 = 5.
    • Problem set from the textbook due on October 24 Friday (submit this through MyLab): 6.6.1, 6.6.2, 6.6.5, 6.6.7, 6.6.9, 6.6.15, 6.6.19, 6.6.21, 6.6.23, 6.6.25, 6.6.27, 6.6.29, 6.6.31, 6.6.39, 6.6.43, 6.6.45, 6.6.49, 6.6.57, 6.6.61.
23. Compound interest: A basic application of exponents and logarithms to finance.
    • Objectives:
      • Calculate simple interest;
      • Calculate intermittent compound interest;
      • Calculate continuous compound interest;
      • Calculate the present value of money;
      • Calculate the interest needed to multiply an amount of money;
      • Calculate the time needed to multiply an amount of money.
    • Reading:
      • Section 6.7 (pages 481–487) from the textbook;
      • My online notes on compound interest.
    • Reading homework due on October 24 Friday (submit this in class or on Canvas):
      1. The original amount of money that earns interest is the _____.
      2. If you borrow P dollars at 100r % annual interest compounded n times per year, then how much will you owe after t years (if you make no payments)?
    • Problem set from the textbook due on October 27 Monday (submit this through MyLab): 6.7.1, 6.7.2, 6.7.7, 6.7.11, 6.7.13, 6.7.15, 6.7.21, 6.7.31, 6.7.33, 6.7.41, 6.7.43.
24. Applications of logarithms: More applications of exponents and logarithms to population growth, radioactive decay, and more.
    • Objectives:
      • Calculate exponential growth or decay;
      • Calculate an exponential growth or decay rate;
      • Calculate a halflife or doubling time;
      • Apply Newton's law of heating and cooling;
      • Apply a formula for logistic growth.
    • Reading:
      • Section 6.8 (pages 494–501) from the textbook;
      • My online notes on applications of logarithms.
    • Reading homework due on October 27 Monday (submit this in class or on Canvas):
      1. Suppose that a quantity A undergoes exponential growth with a relative growth rate of k and an initial value of A₀ at time t = 0. Write down a formula for the value of A as a function of the time t.
      2. Suppose that a quantity A undergoes exponential decay with a halflife of h and an initial value of A₀ at time t = 0. Write down a formula for the value of A as a function of the time t.
    • Problem set from the textbook due on October 29 Wednesday (submit this through MyLab): 6.8.1, 6.8.3, 6.8.5, 6.8.7, 6.8.9, 6.8.11, 6.8.13, 6.8.15, 6.8.17, 6.8.19, 6.8.21, 6.8.23.

Polynomial and rational functions

25. Quadratic functions: One step more complicated than linear functions, we can still graph these precisely.
    • Objectives:
      • Convert the formulas for a quadratic function between standard and general forms;
      • Find the properties of a quadratic function;
      • Graph a quadratic function.
    • Reading:
      • Section 4.3 (pages 299–308) from the textbook;
      • My online notes on quadratic functions.
    • Reading homework due on October 29 Wednesday (submit this in class or on Canvas):
      1. Fill in the blank with a vocabulary word: The shape of the graph of a nonlinear quadratic function is a(n) _____.
      2. Fill in the blanks with algebraic expressions: Given a ≠ 0 and f(x) = ax² + bx + c for all x, the vertex of the graph of f is (___, ___).
      3. Given a ≠ 0, b² − 4ac > 0, and f(x) = ax² + bx + c for all x, how many x-intercepts does the graph of y = f(x) have?
    • Problem set from the textbook due on October 31 Friday (submit this through MyLab): 4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.3.15, 4.3.17, 4.3.19, 4.3.21, 4.3.31, 4.3.33, 4.3.43, 4.3.49, 4.3.53, 4.3.57, 4.3.61, 4.3.63, 4.3.67, 4.3.69.
26. Applications of quadratic functions: Word problems with quadratic functions, especially finding extreme values, including an application to economics.
    • Objectives:
      • Find the maximum or minimum of a quantity by expressing it as a quadratic function of another quantity;
      • Given a demand equation, express revenue as a quadratic function of price or quantity demanded, and maximize it;
      • Given a demand equation and a cost equation, express profit as a quadratic function of price or quantity demanded, and maximize it.
    • Reading:
      • Section 4.4 through Objective 1 (pages 312–316) from the textbook;
      • My online notes on economic applications.
    • Reading homework due on November 5 Wednesday (submit this in class or on Canvas):
      1. Suppose that x and y are variables, x can take any value, and y = ax² + bx + c for some constants a, b, and c.
         1. Fill in the blank with an algebraic equation or inequality: y has a maximum value if _____;
         2. Fill in the blank with an algebraic expression: In this case, y has its maximum when x = ___.
      2. If the width of a rectangle is w metres and its length is l metres, then what is its area (in square metres)?
      3. If you make and sell x items per year at a price of p dollars per item, then what is your revenue (in dollars per year)?
      4. If a business's revenue is R dollars per year and its costs are C dollars per year, then what is its profit (in dollars per year)?
    • Problem set from the textbook due on November 7 Friday (submit this through MyLab): 4.3.87, 4.3.89, 4.3.91, 4.3.93, 4.3.95, 4.4.3, 4.4.5, 4.4.7, 4.4.9, 4.4.11, 4.4.13, 4.4.15.
27. Power functions: Generalizing most of the examples from the library of functions.
    • Objectives:
      • Recognize a power function;
      • Identify key points on the graph of a power function;
      • Graph a power function.
    • Reading:
      • My online notes on power functions;
      • Section 5.1 (pages 331–342) from the textbook.
    • Reading homework due on November 7 Friday (submit this in class or on Canvas): Give the coordinates of:
      1. A point on the graph of every power function;
      2. Another point (different from the answer to #1) on the graph of every power function with a positive exponent;
      3. Another point on the graph of every power function with an even exponent;
      4. Another point on the graph of every power function with an odd exponent.
    • Problem set from the textbook due on November 10 Monday (submit this through MyLab): 5.1.2, 5.1.15, 5.1.17, 5.1.19, 5.1.21, 5.1.27, 5.1.29, 5.1.33.
28. Graphing polynomial functions: Most polynomial functions can't be graphed as thoroughly as quadratic functions, but we'll do our best using their roots.
    • Objectives:
      • Describe the end behaviour of the graph of a polynomial;
      • Find roots of a polynomial by factoring;
      • Find the multiplicity of a root of a factored polynomial;
      • Describe the behaviour of the graph of a polynomial near a root.
    • Reading:
      • My online notes on graphing polynomials (but the last paragraph is optional);
      • Section 5.2 through Objective 1 (pages 346–348) from the textbook.
    • Reading homework due on November 10 Monday (submit this in class or on Canvas):
      1. If a root (aka zero) of a polynomial function has odd multiplicity, then does the graph cross (go through) or only touch (bounce off) the horizontal axis at the intercept given by that root? Which does the graph do if the root has even multiplicity? (Answer both questions!)
      2. If the leading coefficient of a polynomial function is positive, then does the graph's end behaviour go up on the far right, or down? Which does the graph do if the leading coefficient is negative? (Answer both questions!)
    • Problem set from the textbook due on November 12 Wednesday (submit this through MyLab): 5.1.1, 5.1.11, 5.1.41, 5.1.43, 5.1.47, 5.1.49, 5.1.59, 5.1.61, 5.1.69, 5.1.71, 5.1.73, 5.1.75, 5.2.1, 5.2.2, 5.2.5, 5.2.11.
29. Advanced factoring: An advanced factoring technique that will allow you to factor many more polynomials.
    • Objectives:
      • Divide polynomials using synthetic division;
      • Identify potential rational roots of a polynomial;
      • Find the actual roots of a polynomial;
      • Factor a polynomial over the real numbers.
    • Reading:
      • Section R.6 (pages 57–60) from the textbook;
      • Section 5.6 through Objective 1 (pages 387–390) from the textbook;
      • Section 5.6 Objectives 3–5 (pages 391–395) from the textbook.
    • Reading homework due on November 12 Wednesday (submit this in class or on Canvas):
      1. Suppose that f is a polynomial function and c is a number. If you divide f(x) by x − c, then what will the remainder be?
      2. Suppose that f is a polynomial function with rational coefficients and c is an integer. If x − c is a factor of f(x), then what is f(c)?
    • Problem set from the textbook due on November 14 Friday (submit this through MyLab): 5.6.2, 5.6.3, 5.6.4, 5.6.11, 5.6.15, 5.6.19, 5.6.33, 5.6.35, 5.6.37, 5.6.45, 5.6.51, 5.6.53, 5.6.57, 5.6.59, 5.6.65, 5.6.67, 5.6.93, 5.6.99, 5.6.101.
30. Imaginary roots: This is our only use of complex numbers, to help us understand polynomial functions that can't be factored completely over the real numbers.
    • Objectives:
      • Find the complex roots of a polynomial;
      • Reconstruct a polynomial from data about its roots;
      • Factor a polynomial over the complex numbers.
    • Reading:
      • Section 5.7 (pages 401–406) from the textbook.
    • Reading homework due on November 14 Friday (submit this in class or on Canvas): Suppose that f is a polynomial function with real coefficients, a and b are real numbers with b ≠ 0, and the imaginary complex number a + bi is a root (aka zero) of f.
      1. What other complex number must be a root of f?
      2. What non-constant polynomial in x (with real coefficients) must be a factor of f(x)?
    • Problem set from the textbook due on November 17 Monday (submit this through MyLab): 5.7.1, 5.7.2, 5.7.9, 5.7.11, 5.7.13, 5.7.15, 5.7.17, 5.7.19, 5.7.21, 5.7.23, 5.7.25, 5.7.29, 5.7.35, 5.7.39.
31. Rational functions and asymptotes: Dividing two polynomial functions gives us a rational function.
    • Objectives:
      • Reduce a rational function;
      • Find the domain of a rational function;
      • Find the asymptotes of the graph of a rational function.
    • Reading:
      • Section 5.3 (pages 354–361) from the textbook;
      • My online notes on rational functions.
    • Reading homework due on November 17 Monday (submit this in class or on Canvas):
      1. If a graph gets arbitrarily close to a line (without necessarily reaching it) in some direction, then the line is a(n) _____ of the graph.
      2. Suppose that when you divide R(x) = P(x)/‍Q(x), you get a linear quotient q(x) and a linear remainder r(x). (Don't mix up lowercase and uppercase letters here!) Write an equation in x and y for the non-vertical linear asymptote of the graph of R.
    • Problem set from the textbook due on November 19 Wednesday (submit this through MyLab): 5.3.2, 5.3.3, 5.3.4, 5.3.15, 5.3.17, 5.3.19, 5.3.23, 5.3.27, 5.3.29, 5.3.31, 5.3.35, 5.3.45, 5.3.47, 5.3.49, 5.3.51.
32. Graphs of rational functions: Dividing two polynomial functions gives us a rational function.
    • Objectives:
      • Find the holes in the graph of a rational function;
      • Graph a rational function.
    • Reading: Section 5.4 (pages 365–375) from the textbook.
    • Reading homework due on November 19 Wednesday (submit this in class or on Canvas):
      1. If the reduced form of a rational function is defined somewhere where the original (unreduced) form is not, then the graph of the original function has a(n) _____ there.
      2. Suppose that when you divide R(x) = P(x)/‍Q(x), you get a linear quotient q(x) and a linear remainder r(x). (Don't mix up lowercase and uppercase letters here!) Write an equation in x that you might solve to find where the graph of R meets its non-vertical linear asymptote.
    • Problem set from the textbook due on November 21 Friday (submit this through MyLab): 5.4.1, 5.4.5, 5.4.7, 5.4.9, 5.4.11, 5.4.17, 5.4.19, 5.4.21, 5.4.23, 5.4.31, 5.4.33, 5.4.35, 5.4.51, 5.4.53.

Quizzes

1. Graphs and functions:
   • Review date: September 12 Friday.
   • Date due: September 15 Monday.
   • Corresponding problem sets: 1–8.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show in Section WBP02: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #9. (You may use any method to solve the problems, even if the instructions say to use a particular method.)
2. Properties and types of functions:
   • Review date: October 10 Friday.
   • Date due: October 15 Wednesday.
   • Corresponding problem sets: 9–17.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show in Section WBP02: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #2, #7, and #8.
3. Exponential and logarithmic functions:
   • Review date: October 31 Friday.
   • Date due: November 3 Monday.
   • Corresponding problem sets: 18–24.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show in Section WBP02: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #2.
4. Polynomial and rational functions:
   • Review date: November 21 Friday.
   • Date due: November 24 Monday.
   • Corresponding problem sets: 25–32.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show in Section WBP02: Submit a picture of your work on Canvas, at least one intermediate step for each result except for those in #3 and #4.

Final exam

For the exam, you may use one sheet of notes that you wrote yourself; please take a scan or a picture of this (both sides) and submit it here on Canvas. However, you may not use your book or anything else not written by you. You certainly should not talk to other people! Calculators are allowed (although you shouldn't really need one), but not communication devices (like cell phones).

The exam consists of questions similar in style and content to those in the practice exam (DjVu).

The final exam is proctored. If you're near any of the three main SCC campuses (Lincoln, Beatrice, Milford), then you can schedule the exam at one of the Testing Centers; it will automatically be ready for you at Lincoln, but let me know if you plan to take it at Beatrice or Milford, so that I can have it ready for you there. If you have access to a computer with a webcam and mike, then you can take it using ProctorU for an additional fee; let me know if you want to do this so that I can send you an invitation to schedule it. If you're near Lincoln, then we may be able to schedule a time for you to take the exam with me in person. If none of these will work for you, then contact me as soon as possible!

To take the actual exam online, hit Next, or use this direct link. (You will need an access code, which you should get from your proctor.)

The permanent URI of this web page is https://tobybartels.name/MATH-1150/2025FA/.