MATH-1150-WBP01

Course administration

• Canvas page (where you must log in).
• Help with DjVu (if you have trouble reading the DjVu files on this page).
• Official syllabus (DjVu).
• 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:
  • on Mondays, Wednesdays, and Fridays from 11:00 to 12:00,
  • on Tuesdays and Thursdays from 2:30 PM to 3:30, and
  • by appointment,
  in room U9C and over Zoom meeting 610-024-2876.

Readings

Graphs and functions

1. General review:
   • Reading:
     • My online introduction;
     • Skim Chapter R (except Section R.6) and Chapter 1 (except Section 1.6) from the textbook, and review anything that you are shaky on.
   • Exercises due on January 24 Wednesday (submit these on Canvas):
     1. Which of the following are equations?
        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.
   • Discuss this in Discussion 1 on Canvas.
   • Exercises from the textbook due on January 26 Friday (submit these 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, 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 points:
   • Reading: Section 2.1 (pages 150–154) from the textbook.
   • Exercises due on January 26 Friday (submit these 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 blank with a number: If the legs of a right triangle have lengths 3 and 4, then the length of its hypotenuse is ___.
     3. Fill in the blanks with algebraic expressions: The distance between the points (x₁, y₁) and (x₂, y₂) is _____, and the midpoint between them is (___, ___).
   • Discuss this in Discussion 2 on Canvas.
   • Exercises from the textbook due on January 29 Monday (submit these through MyLab): 2.1.4, 2.1.15, 2.1.17, 2.1.19, 2.1.21, 2.1.23, 2.1.27, 2.1.33, 2.1.39, 2.1.43, 2.1.47, 2.1.63, 2.1.71.
3. Graphing equations:
   • Reading:
     • Section 2.2 (pages 157–164) from the textbook;
     • My online notes on symmetry and intercepts.
   • Exercises due on January 29 Monday (submit these on Canvas): Fill in the blanks with vocabulary words:
     1. 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.
     2. 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 _____.
   • Discuss this in Discussion 3 on Canvas.
   • Exercises from the textbook due on January 31 Wednesday (submit these through MyLab): 2.2.1, 2.2.2, 2.2.7, 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.
4. Lines:
   • Reading:
     • Section 2.3 (pages 169–179) from the textbook;
     • My online notes on lines and line segments.
   • Exercises due on January 31 Wednesday (submit these on Canvas): Fill in the blanks with words or numbers:
     1. Write an equation for the line in the (x, y)-plane with slope m and y-intercept (0, b).
     2. The slope of a vertical line is _____, and the slope of a horizontal line is _____.
     3. 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 ___.
   • Discuss this in Discussion 4 on Canvas.
   • Exercises from the textbook due on February 2 Friday (submit these through MyLab): 2.3.2, 2.3.7, 2.3.8, 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, 2.3.51, 2.3.53, 2.3.57, 2.3.63, 2.3.67, 2.3.73, 2.3.75, 2.3.79, 2.3.85, 2.3.91, 2.3.93, 2.3.111, 2.3.113.
5. Systems of equations:
   • Reading:
     • Section 12.1 (pages 868–878) from the textbook;
     • My online notes and video on systems of equations.
   • Exercises due on February 2 Friday (submit these on Canvas):
     1. 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?
     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?
   • Discuss this in Discussion 5 on Canvas.
   • Exercises from the textbook due on February 5 Monday (submit these through MyLab): 12.1.3, 12.1.4, 12.1.6, 12.1.11, 12.1.13, 12.1.15, 12.1.17, 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. Functions:
   • Reading:
     • Section 3.1 through Objective 4 (pages 203–211) from the textbook;
     • My online notes on functions.
   • Exercises due on February 5 Monday (submit these 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 | _____}.
   • Discuss this in Discussion 6 on Canvas.
   • Exercises from the textbook due on February 7 Wednesday (submit these through MyLab): 3.1.1, 3.1.2, 3.1.33, 3.1.35, 3.1.43, 3.1.49, 3.1.103.
7. Operations on functions:
   • Reading: The rest of Section 3.1 (pages 211–215) from the textbook.
   • Exercises due on February 7 Wednesday (submit these on Canvas):
     1. 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 _____.
     2. 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.
   • Discuss this in Discussion 7 on Canvas.
   • Exercises from the textbook due on February 9 Friday (submit these through MyLab): 3.1.3, 3.1.10, 3.1.51, 3.1.53, 3.1.55, 3.1.59, 3.1.63, 3.1.71, 3.1.79, 3.1.81.
8. Graphs of functions:
   • Reading: Section 3.2 (pages 219–223) from the textbook.
   • Exercises due on February 9 Friday (submit these on Canvas):
     1. Fill in the blanks with mathematical expressions: If (3, 5) 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. True or false: The graph of a function can have any number of x-intercepts.
     4. True or false: The graph of a function can have any number of y-intercepts.
   • Discuss this in Discussion 8 on Canvas.
   • Exercises from the textbook due on February 12 Monday (submit these through MyLab): 3.2.7, 3.2.9, 3.2.11, 3.2.13, 3.2.15, 3.2.17, 3.2.19, 3.2.21, 3.2.27, 3.2.29, 3.2.31, 3.2.33, 3.2.39, 3.2.45, 3.2.47.
9. Properties of functions:
   • Reading:
     • Section 3.3 through Objective 2 (pages 229–231) from the textbook;
     • My online notes on properties of functions.
   • Exercises due on February 12 Monday (submit these 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.
   • Discuss this in Discussion 9 on Canvas.
   • Exercises from the textbook due on February 14 Wednesday (submit these 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:
    • Reading: The rest of Section 3.3 (pages 231–237) from the textbook.
    • Exercises due on February 14 Wednesday (submit these 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.
    • Discuss this in Discussion 10 on Canvas.
    • Exercises from the textbook due on February 16 Friday (submit these through MyLab): 3.3.2, 3.3.13, 3.3.15, 3.3.17, 3.3.19, 3.3.21, 3.3.23, 3.3.26, 3.3.27, 3.3.29, 3.3.31, 3.3.49, 3.3.51.
11. Word problems with functions:
    • Reading:
      • Section 3.6 (pages 267–269) from the textbook;
      • My online notes and video on functions in word problems.
    • Exercise due on February 16 Friday (submit this 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.)
    • Discuss this in Discussion 11 on Canvas.
    • Exercises from the textbook due on February 19 Monday (submit these through MyLab): 3.6.5, 3.6.13, 3.6.15, 3.6.21, 3.6.23.

Types of functions

12. Linear functions:
    • Reading: Section 4.1 (pages 281–287) from the textbook.
    • Exercises due on February 19 Monday (submit these 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(a) and f(b) for two distinct real numbers a and b, then give a formula for the slope of the graph of f using a, b, f(a), and/or f(b).
    • Discuss this in Discussion 12 on Canvas.
    • Exercises from the textbook due on February 21 Wednesday (submit these 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:
    • Reading: Section 3.4 Objective 1 (pages 242–246) from the textbook.
    • Exercises due on February 21 Wednesday (submit these on Canvas): Fill in the blanks with vocabulary words:
      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.
    • Discuss this in Discussion 13 on Canvas.
    • Exercises from the textbook due on February 23 Friday (submit these through MyLab): 3.4.9, 3.4.11–18, 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:
    • Reading:
      • My online notes and video on partially-defined functions;
      • The rest of Section 3.4 (pages 247–249) from the textbook.
    • Exercises due on February 28 Wednesday (submit these 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.
    • Discuss this in Discussion 14 on Canvas.
    • Exercises from the textbook due on March 1 Friday (submit these 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:
    • Reading:
      • Section 6.1 (pages 415–419) from the textbook;
      • My online notes on composite functions.
    • Exercises due on March 1 Friday (submit these 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.
    • Discuss this in Discussion 15 on Canvas.
    • Exercises from the textbook due on March 4 Monday (submit these 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:
    • Reading:
      • Section 6.2 (pages 423–430) from the textbook;
      • My online notes on inverse functions.
    • Exercises due on March 4 Monday (submit these 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.
    • Discuss this in Discussion 16 on Canvas.
    • Exercises from the textbook due on March 6 Wednesday (submit these 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, 6.2.27, 6.2.29, 6.2.31, 6.2.35, 6.2.37, 6.2.41, 6.2.43, 6.2.45, 6.2.55, 6.2.57, 6.2.59, 6.2.61, 6.2.75, 6.2.77, 6.2.79, 6.2.87.
17. Coordinate transformations:
    • Reading:
      • Section 3.5 (pages 254–263) from the textbook;
      • My online notes on linear coordinate transformations.
    • Exercises due on March 6 Wednesday (submit these on Canvas): Assume that the axes are oriented in the usual way (positive x-axis to the right, 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?
    • Discuss this in Discussion 17 on Canvas.
    • Exercises from the textbook due on March 8 Friday (submit these through MyLab): 3.5.5, 3.5.6, 3.5.7–10, 3.5.11–14, 3.5.15–18, 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.
18. Quadratic functions:
    • Reading:
      • Section 4.3 (pages 299–308) from the textbook;
      • My online notes on quadratic functions.
    • Exercises due on March 8 Friday (submit these 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?
    • Discuss this in Discussion 18 on Canvas.
    • Exercises from the textbook due on March 18 Monday (submit these through MyLab): 4.3.1, 4.3.2, 4.3.3, 4.3.4, 4.3.15–22, 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, 4.3.70.
19. Applications of quadratic functions:
    • Reading: Section 4.4 through Objective 1 (pages 312–316) from the textbook.
    • Exercises due on March 18 Monday (submit these on Canvas): Suppose that x and y are variables, 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 = ___.
    • Discuss this in Discussion 19 on Canvas.
    • Exercises from the textbook due on March 20 Wednesday (submit these through MyLab): 4.3.93, 4.3.95, 4.4.7, 4.4.9, 4.4.11, 4.4.13, 4.4.15.
20. Applications to economics:
    • Reading: My online notes on economic applications.
    • Exercises due on March 20 Wednesday (submit these on Canvas):
      1. 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)?
      2. 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)?
    • Discuss this in Discussion 20 on Canvas.
    • Exercises from the textbook due on March 22 Friday (submit these through MyLab): 4.3.87, 4.3.89, 4.4.3, 4.4.5.
21. Exponential functions:
    • Reading:
      • Section 6.3 (pages 435–446) from the textbook;
      • My online notes on exponential functions.
    • Exercises due on March 22 Friday (submit these on Canvas): Let f(x) be Cb^x for all x.
      1. What is f(x + 1)/f(x)?
      2. What are f(−1), f(0), and f(1)?
      (Write your answers using b and/or C, and simplify them as much as possible.)
    • Discuss this in Discussion 21 on Canvas.
    • Exercises from the textbook due on March 25 Monday (submit these through MyLab): 6.3.1, 6.3.15, 6.3.16, 6.3.21, 6.3.23, 6.3.25, 6.3.27, 6.3.29, 6.3.31, 6.3.33, 6.3.35, 6.3.37–44, 6.3.45, 6.3.47, 6.3.51, 6.3.53, 6.3.57, 6.3.59, 6.3.61, 6.3.65, 6.3.67, 6.3.71, 6.3.73, 6.3.76, 6.3.77, 6.3.79, 6.3.83, 6.3.85, 6.3.91, 6.3.93.
22. Logarithmic functions:
    • Reading:
      • Section 6.4 through Objective 4 (pages 452–457) from the textbook;
      • Section 6.4 Summary (page 460) from the textbook;
      • My online notes on logarithmic functions.
    • Exercises due on March 25 Monday (submit these 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)?
    • Discuss this in Discussion 22 on Canvas.
    • Exercises from the textbook due on March 27 Wednesday (submit these through MyLab): 6.4.11, 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, 6.4.43, 6.4.51, 6.4.53, 6.4.55, 6.4.57, 6.4.65–72, 6.4.73, 6.4.79, 6.4.83, 6.4.85.

Logarithms and polynomials

23. More about logarithms:
    • Reading:
      • Section 6.4 Objective 5 (pages 457–460) from the textbook;
      • Section 6.5 Objective 4 (pages 469–471) from the textbook.
    • Exercises due on April 3 Wednesday (submit these on Canvas): Given 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).
    • Discuss this in Discussion 23 on Canvas.
    • Exercises from the textbook due on April 5 Friday (submit these through MyLab): 6.4.89, 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, 6.4.119, 6.4.129, 6.4.131, 6.5.7, 6.5.11, 6.5.71, 6.5.73, 6.5.75, 6.5.78.
24. Properties of logarithms:
    • 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.
    • Exercises due on April 5 Friday (submit these on Canvas): 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) = ___.
    • Discuss this in Discussion 24 on Canvas.
    • Exercises from the textbook due on April 8 Monday (submit these 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.
25. Logarithmic equations:
    • Reading: Section 6.6 (pages 474–478) from the textbook.
    • Exercises due on April 8 Monday (submit these 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.
    • Discuss this in Discussion 25 on Canvas.
    • Exercises from the textbook due on April 10 Wednesday (submit these 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.
26. Compound interest:
    • Reading:
      • Section 6.7 (pages 481–487) from the textbook;
      • My online notes on compound interest.
    • Exercises due on April 10 Wednesday (submit these 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)?
    • Discuss this in Discussion 26 on Canvas.
    • Exercises from the textbook due on April 12 Friday (submit these 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.
27. Applications of logarithms:
    • Reading:
      • Section 6.8 (pages 478–485) from the textbook;
      • My online notes on applications of logarithms.
    • Exercises due on April 12 Friday (submit these 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.
    • Discuss this in Discussion 27 on Canvas.
    • Exercises from the textbook due on April 15 Monday (submit these 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.
28. Power functions:
    • Reading: Section 5.1 through Objective 2 (pages 331–336) from the textbook.
    • Exercises due on April 15 Monday (submit these on Canvas): For any real number n, the power function with exponent n is the function f such that f(x) = xⁿ for all possible x. Give the coordinates of:
      1. A point on the graph of every power function;
      2. Another point (different from the answer to the previous part) 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; and
      4. Another point on the graph of every power function with an odd exponent.
    • Discuss this in Discussion 28 on Canvas.
    • Exercises from the textbook due on April 17 Wednesday (submit these 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.
29. Graphing polynomials:
    • Reading:
      • The rest of Section 5.1 (pages 336–342) from the textbook;
      • My online notes on graphing polynomials (but the last paragraph is optional);
      • Section 5.2 Objective 1 (pages 346–348) from the textbook.
    • Exercises due on April 17 Wednesday (submit these 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?
      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?
    • Discuss this in Discussion 29 on Canvas.
    • Exercises from the textbook due on April 19 Friday (submit these 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.
30. Advanced factoring:
    • 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.
    • Exercises due on April 19 Friday (submit these 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)?
    • Discuss this in Discussion 30 on Canvas.
    • Exercises from the textbook due on April 22 Monday (submit these 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.
31. Imaginary roots:
    • Reading: Section 5.7 (pages 401–406) from the textbook.
    • Exercises due on April 22 Monday (submit these on Canvas): Suppose that f is a polynomial function with real coefficients, a and b are real numbers with b ≠ 0, and the 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)?
    • Discuss this in Discussion 31 on Canvas.
    • Exercises from the textbook due on April 24 Wednesday (submit these 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.
32. Rational functions and asymptotes:
    • Reading:
      • Section 5.3 (pages 354–361) from the textbook;
      • My online notes on rational functions.
    • Exercises due on April 24 Wednesday (submit these 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). Write an equation in x and y for the non-vertical linear asymptote of the graph of R. (Warning: Don't mix up lowercase and uppercase letters in your answer!)
    • Discuss this in Discussion 32 on Canvas.
    • Exercises from the textbook due on April 26 Friday (submit these 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.
33. Graphs of rational functions:
    • Reading: Section 5.4 (pages 365–375) from the textbook.
    • Exercises due on April 26 Friday (submit these 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). Write an equation in x that you might solve to find where the graph of R meets this asymptote. (Warning: Don't mix up lowercase and uppercase letters in your answer!)
    • Discuss this in Discussion 33 on Canvas.
    • Exercises from the textbook due on April 29 Monday (submit these 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.
34. Inequalities:
    • Reading:
      • Section 5.5 (pages 380–384) from the textbook;
      • My online notes on solving inequalities.
    • Exercise due on April 29 Monday (submit this on Canvas): Suppose that you have a rational inequality in one variable that you wish to solve. You investigate the inequality and discover the following facts about it:
      • the left-hand side is always defined;
      • the right-hand side is undefined when x is 2 but is otherwise defined;
      • the left-hand side and right-hand side are equal when x is −3/2 and only then;
      • the original inequality is true when x is −3/2 or 3 but false when x is −2 or 0.
      What are the solutions to the inequality?
    • Discuss this in Discussion 34 on Canvas.
    • Exercises from the textbook due on May 1 Wednesday (submit these through MyLab): 5.5.1, 5.5.5, 5.5.7, 5.5.9, 5.5.13, 5.5.15, 5.5.19, 5.5.21, 5.5.23, 5.5.27, 5.5.29, 5.5.35, 5.5.39, 5.5.41, 5.5.43, 5.5.47.

Quizzes

1. Graphs and functions:
   • Date available: February 23 Friday.
   • Date due: February 26 Monday.
   • Corresponding problem sets: 1–11.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except in #8 and #10. (You may use any method to solve the problems, even if the instructions say to use a particular method.)
2. Types of functions:
   • Date available: March 29 Friday.
   • Date due: April 1 Monday.
   • Corresponding problem sets: 12–22.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except in #4, #5, #8, and #9.
3. Logarithms and polynomials:
   • Date available: May 3 Friay.
   • Date due: May 6 Monday.
   • Corresponding problem sets: 23–34.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
   • Work to show: Submit a picture of your work on Canvas, at least one intermediate step for each result except in #5.

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 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 will be proctored. If you have access to a computer with a webcam, then you can schedule a time with me to take the exam in a Zoom meeting. If you're near Lincoln, then we can schedule a time for you to take the exam in person. If you're near any of the three main SCC campuses (Lincoln, Beatrice, Milford) and available on a weekday, then you can schedule the exam at one of the Testing Centers. If none of these will work for you, then contact me as soon as possible to make alternate arrangements.

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