MATH-1150-LN01&LN06

Welcome to the permanent home page for Sections LN01 and LN06 of MATH-1150 (College Algebra) at Southeast Community College in the Fall term of 2022. I am Toby Bartels, your instructor.

For Section LN01

• Official syllabus (DjVu).
• Course policies (DjVu).
• Class hours: Mondays, Wednesday, and Fridays from 9:00 to 9:50 in LNK U105.
• Final exam: December 14 Wednesday from 12:00 to 1:40 PM in ESQ 100C (or by appointment).

For Section LN06

• Official syllabus (DjVu).
• Course policies (DjVu).
• Class hours: Tuesdays and Thursdays from 3:00 PM to 4:20 in LNK U107.
• Final exam: December 14 Wednesday from 12:00 to 1:40 PM in ESQ 100C (or by appointment).

Contact information

Feel free to send a message at any time, even nights and weekends (although I'll be slower to respond then).

The official textbook for the course is the 11th Edition of Algebra & Trigonometry by Sullivan published by Prentice-Hall (Pearson). You automatically get an online version of this textbook through Canvas, although you can use a print version instead if you like. This comes with access to Pearson MyLab, integrated into Canvas, on which many of the assignments appear.

Graphs and functions

1. General review:
• 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 August 24 Wednesday (submit these on Canvas or in class):
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 = 1 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.
• Exercises from the textbook due on August 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 August 26 Friday (submit these on Canvas or in class):
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 (___, ___).
• Exercises from the textbook due on August 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:
• Exercises due on August 29 Monday (submit these on Canvas or in class): 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 _____.
• Exercises from the textbook due on August 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:
• Exercises due on August 31 Wednesday (submit these on Canvas or in class): 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 _____.
• Exercises from the textbook due on September 2 Friday (submit these through MyLab): 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.
5. Linear equations:
• The rest of Section 2.3 (pages 176–179) from the textbook;
• The introduction to Section 12.1 (pages 868–870) from the textbook.
• Exercises due on September 2 Friday (submit these on Canvas or in class):
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?
• Exercises from the textbook due on September 7 Wednesday (submit these 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.
6. Systems of equations:
• The rest of Section 12.1 (pages 871–878) from the textbook;
• My online notes and video on systems of equations.
• Exercises due on September 7 Wednesday (submit these on Canvas or in class): 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?
• Exercises from the textbook due on September 9 Friday (submit these 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.
7. Functions:
• Section 3.1 through Objective 4 (pages 203–211) from the textbook;
• My online notes on functions.
• Exercises due on September 9 Friday (submit these on Canvas or in class):
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 | _____}.
• Exercises from the textbook due on September 12 Monday (submit these through MyLab): 3.1.1, 3.1.2, 3.1.31, 3.1.33, 3.1.35, 3.1.43, 3.1.49, 3.1.103.
8. Operations on functions:
• Reading: The rest of Section 3.1 (pages 211–215) from the textbook.
• Exercises due on September 12 Monday (submit these on Canvas or in class):
1. Fill in the blanks with vocabulary words: If f(3) = 5, then 3 belongs to the _____ of the function, 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.
• Exercises from the textbook due on September 14 Wednesday (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.
9. Graphs of functions:
• Reading: Section 3.2 (pages 219–223) from the textbook.
• Exercises due on September 14 Wednesday (submit these on Canvas or in class):
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.
• Exercises from the textbook due on September 16 Friday (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.
Quiz 1, covering the material in Problem Sets 1–9, is on September 26 Monday.

Properties and types of functions

1. Properties of functions:
• Exercises due on September 16 Friday (submit these on Canvas or in class): 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.
• Exercises from the textbook due on September 19 Monday (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.
2. Rates of change:
• Reading: The rest of Section 3.3 (pages 231–237) from the textbook.
• Exercises due on September 19 Monday (submit these on Canvas or in class): 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.
• Exercises from the textbook due on September 21 Wednesday (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.
3. Word problems with functions:
• Exercise due on September 21 Wednesday (submit this on Canvas or in class): 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.).
• Exercises from the textbook due on September 23 Friday (submit these through MyLab): 3.6.5, 3.6.13, 3.6.15, 3.6.21, 3.6.23.
4. Linear functions:
• Reading: Section 4.1 (pages 281–287) from the textbook.
• Exercises due on September 28 Wednesday (submit these on Canvas or in class):
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 f(b).
• Exercises from the textbook due on September 30 Friday (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.
5. The library of functions:
• Reading: Section 3.4 Objective 1 (pages 242–246) from the textbook.
• Exercises due on September 30 Friday (submit these on Canvas or in class): 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.
• Exercises from the textbook due on October 3 Monday (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.
6. Piecewise-defined functions:
• Exercises due on October 3 Monday (submit these on Canvas or in class): 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.
• Exercises from the textbook due on October 5 Wednesday (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.
7. Composite functions:
• Exercises due on October 5 Wednesday (submit these on Canvas or in class):
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.
• Exercises from the textbook due on October 7 Friday (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.
8. Inverse functions:
• Section 6.2 through Objective 1 (pages 423–425) from the textbook;
• Section 6.2 Objectives 3&4 (pages 427–430) from the textbook;
• My online notes on inverse functions.
• Exercises due on October 7 Friday (submit these on Canvas or in class):
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.
• Exercises from the textbook due on October 10 Monday (submit these through MyLab): 6.2.4, 6.2.5, 6.2.7, 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, 6.2.87.
9. Graphs of inverse functions:
• Reading: Section 6.2 Objective 2 (page 426) from the textbook.
• Exercises due on October 10 Monday (submit these on Canvas or in class):
1. 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.
2. 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.
• Exercises from the textbook due on October 12 Wednesday (submit these through MyLab): 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, 6.2.77, 6.2.79.
10. Coordinate transformations:
• Exercises due on October 12 Wednesday (submit these on Canvas or in class): 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?
• Exercises from the textbook due on October 14 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.
• Exercises due on October 14 Friday (submit these on Canvas or in class):
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?
• Exercises from the textbook due on October 19 Wednesday (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.
• Reading: Section 4.4 through Objective 1 (pages 312–316) from the textbook.
• Exercises due on October 19 Wednesday (submit these on Canvas or in class): 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 = ___.
• Exercises from the textbook due on October 21 Friday (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.
13. Applications to economics:
• Reading: My online notes on economic applications.
• Exercises due on October 21 Friday (submit these on Canvas or in class):
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)?
• Exercises from the textbook due on October 24 Monday (submit these through MyLab): 4.3.87, 4.3.89, 4.4.3, 4.4.5.
Quiz 2, covering the material in Problem Sets 10–22, is on October 31 Monday.

Logarithms and polynomials

1. Exponential functions:
• Exercises due on October 24 Monday (submit these on Canvas or in class): Let f(x) be Cbx 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.)
• Exercises from the textbook due on October 26 Wednesday (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.
2. Logarithmic functions:
• Exercises due on October 26 Wednesday (submit these on Canvas or in class): Suppose that b > 0 and b ≠ 1.
1. Rewrite logbM = r as an equation involving exponentiation.
2. What are logbb, logb 1, and logb (1/b)?
• Exercises from the textbook due on October 28 Friday (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, 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.
3. Properties of logarithms:
• Exercises due on November 2 Wednesday (submit these on Canvas or in class): 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. logb (uv) = ___.
2. logb (u/v) = ___.
3. logb (ux) = ___.
• Exercises from the textbook due on November 4 Friday (submit these through MyLab): 6.5.7, 6.5.11, 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, 6.5.71, 6.5.73, 6.5.75, 6.5.78, 6.5.87, 6.5.91, 6.5.97.
4. Logarithmic equations:
• Reading: Section 6.6 (pages 474–478) from the textbook.
• Exercises due on November 4 Friday (submit these on Canvas or in class): 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. 2x+3 = 5.
• Exercises from the textbook due on November 7 Monday (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.
5. Compound interest:
• Section 6.7 (pages 481–487) from the textbook;
• My online notes on compound interest.
• Exercises due on November 7 Monday (submit these on Canvas or in class):
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)?
• Exercises from the textbook due on November 9 Wednesday (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.
6. Applications of logarithms:
• Exercise due on November 9 Wednesday (submit this on Canvas or in class): 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.
• Exercises from the textbook due on November 11 Friday (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.
7. Power functions:
• Reading: Section 5.1 through Objective 2 (pages 331–336) from the textbook.
• Exercises due on November 11 Friday (submit these on Canvas or in class): 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; and
4. Another point on the graph of every power function with an odd exponent.
• Exercises from the textbook due on November 14 Monday (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.
8. Graphing polynomials:
• 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 November 14 Monday (submit these on Canvas or in class):
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?
• Exercises from the textbook due on November 16 Wednesday (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.
• 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 November 16 Wednesday (submit these on Canvas or in class):
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)?
• Exercises from the textbook due on November 18 Friday (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.
10. Imaginary roots:
• Reading: Section 5.7 (pages 401–406) from the textbook.
• Exercises due on November 18 Friday (submit these on Canvas or in class): 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 polynomial in x (with real coefficients) must be a factor of f(x)?
• Exercises from the textbook due on November 21 Monday (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.
11. Rational functions and asymptotes:
• Exercises due on November 21 Monday (submit these on Canvas or in class):
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!)
• Exercises from the textbook due on November 28 Monday (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.
12. Graphs of rational functions:
• Reading: Section 5.4 (pages 365–375) from the textbook.
• Exercises due on November 28 Monday (submit these on Canvas or in class):
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 crosses its non-vertical linear asymptote. (Warning: Don't mix up lowercase and uppercase letters in your answer!)
• Exercises from the textbook due on November 30 Wednesday (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.
13. Inequalities:
• Exercise due on November 30 Wednesday (submit this on Canvas or in class): 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?
• Exercises from the textbook due on December 2 Friday (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.
Quiz 3, covering the material in Problem Sets 23–35, is on December 5 Monday.

Quizzes

1. Graphs and functions:
• Review date: September 23 Friday (in class).
• Date taken: September 26 Monday (in class).
• Corresponding problem sets: 1–9.
• Help allowed: Your notes, calculator.
• NOT allowed: Textbook, my notes, other people, websites, etc.
2. Properties and types of functions:
• Review date: October 28 Friday (in class).
• Date taken: October 31 Monday (in class).
• Corresponding problem sets: 10–22.
• Help allowed: Your notes, calculator.
• NOT allowed: Textbook, my notes, other people, websites, etc.
3. Logarithms and polynomials:
• Review date: December 2 Friday (in class).
• Date taken: December 5 Monday (in class).
• Corresponding problem sets: 23–35.
• Help allowed: Your notes, calculator.
• NOT allowed: Textbook, my notes, other people, websites, etc.

Final exam

There is a comprehensive final exam on December 14 Wednesday, in our normal classroom at the normal time but lasting until 10:40. (You can also arrange to take it at a different time December 12–16.) To speed up grading at the end of the term, the exam is multiple choice and filling in blanks, with no partial credit.

For the exam, you may use one sheet of notes that you wrote yourself. 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 final exam:

This web page and the files linked from it (except for the official syllabus) were written by Toby Bartels, last edited on 2022 December 23. Toby reserves no legal rights to them.

The permanent URI of this web page is `https://tobybartels.name/MATH-1150/2022FA/`.