- 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: Mondays, Wednesdays, and Friday from 11:00 to 11:50 in room U105.
- Final exam: December 9 Monday from 11:00 to 12:40 in room U105.

- 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 1:00 PM to 2:00,
- on Tuesdays and Thursdays from 10:30 to 11:30, and
- by appointment,

- 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're shaky on.

- Exercises due on August 21 Wednesday
(submit these on Canvas or in class):
- Which of the following are
*equations*? (Say Yes or No for each.)- 2
*x*+*y*; - 2
*x*+*y*= 0; *z*= 2*x*+*y*.

- 2
- You probably don't know how to
*solve*the equation*x*^{5}+ 2*x*= 1, but show what numerical calculation you make to*check*whether*x*= 2 is a solution. - Write the set {
*x*|*x*< 3} in interval notation and draw a graph of the set. - Suppose that
*a**x*^{2}+*b**x*+*c*= 0 but*a*≠ 0; write down a formula for*x*.

- Which of the following are
- Exercises from the textbook due on August 23 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.

- Reading:
- Graphing review:
- 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.

- Exercises due on August 23 Friday (submit these on Canvas or in class):
- 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 _____.
- 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.
- 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 _____.

- Exercises from the textbook due on August 26 Monday (submit these 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.

- Reading:
- Graphing 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.

- Exercises due on August 26 Monday (submit these on Canvas or in class):
- Fill in the blanks with algebraic expressions:
The distance between the points
(
*x*_{1},*y*_{1}) and (*x*_{2},*y*_{2}) is _____, and the midpoint between them is (___, ___). - Write an equation
for the line in the (
*x*,*y*)-plane with slope*m*and*y*-intercept (0,*b*). - Fill in the blanks with words or numbers: The slope of a vertical line is _____, and the slope of a horizontal line is _____.

- Fill in the blanks with algebraic expressions:
The distance between the points
(
- Exercises from the textbook due on August 28 Wednesday (submit these 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.

- Reading:
- Linear equations:
- Reading:
- 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 August 28 Wednesday (submit these on Canvas or in class):
- 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 ___. - 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?

- Fill in the blanks with numbers:
Suppose that a line
- Exercises from the textbook due on August 30 Friday (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.

- Reading:
- Systems of equations:
- Reading:
- The rest of Section 12.1 (pages 871–878) from the textbook;
- My online notes and video on systems of equations.

- Exercises due on August 30 Friday (submit these on Canvas or in class):
- 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*.) - Consider the system of equations
consisting of
*x*+ 3*y*= 4 (equation 1) and 2*x*+ 3*y*= 5 (equation 2).- If I solve equation (1) for
*x*to get*x*= 4 − 3*y*and apply this to equation (2) to get 2(4 − 3*y*) + 3*y*= 5 (and continue from there), then what method am I using to solve this system? - If instead I multiply equation (1) by −2
to get −2
*x*− 6*y*= −8 and combine this with equation (2) to get −3*y*= −3 (and continue from there), then what method am I using to solve this system?

- If I solve equation (1) for

- Given a system of two equations
in the two variables
- Exercises from the textbook due on September 4 Wednesday (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.

- Reading:
- Systems of inequalities:
- Reading: Section 12.7 (pages 942–947) from the textbook.
- Exercises due on September 4 Wednesday
(submit these on Canvas or in class):
- Fill in the blank: If a system of equations or inequalities has no solutions, then the system is _____.
- When graphing an inequality in two variables, if the inequality is strict (written with < or >, instead of ≤ or ≥), then should the boundary be solid or dashed?

- Exercises from the textbook due on September 6 Friday (submit these 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.

- Functions:
- Reading:
- Section 3.1 (pages 203–215) from the textbook;
- My online notes on functions.

- Exercises due on September 6 Friday (submit these on Canvas or in class):
- Fill in the blank with a mathematical expression:
If
*g*(*x*) = 2*x*+ 3 for all*x*, then*g*(___) = 2(5) + 3 = 13. - 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 | _____}. - 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 _____. - Fill in the blank with an arithmetic operation:
If
*f*(*x*) = 2*x*for all*x*, and*g*(*x*) = 3*x*for all*x*, then (*f*___*g*)(*x*) = 5*x*for all*x*.

- Fill in the blank with a mathematical expression:
If
- Exercises from the textbook due on September 9 Monday (submit these 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.

- Reading:
- Graphs of functions:
- Reading: Section 3.2 (pages 219–223) from the textbook.
- Exercises due on September 9 Monday (submit these on Canvas or in class):
- Fill in the blanks with mathematical expressions:
If (3, 5) is a point on the graph of a function
*f*, then*f*(___) = ___. - 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.
- Which of these is true, and which of these is false?
- The graph of a function
can have any number of
*x*-intercepts; - The graph of a function
can have any number of
*y*-intercepts.

- The graph of a function
can have any number of

- Fill in the blanks with mathematical expressions:
If (3, 5) is a point on the graph of a function
- Exercises from the textbook due on September 11 Wednesday (submit these 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 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 September 11 Wednesday
(submit these on Canvas or in class):
Fill in the blanks with vocabulary words:
- Suppose that
*f*is a function and, whenever*f*(*x*) exists, then*f*(−*x*) also exists and equals*f*(*x*). Then*f*is _____. - If
*c*is a number and*f*is a function, and if*f*(*c*) = 0, then*c*is a(n) _____ of*f*.

- Suppose that
- Exercises from the textbook due on September 13 Friday (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.

- Reading:
- Rates of change:
- Reading: The rest of Section 3.3 (pages 231–237) from the textbook.
- Exercises due on September 18 Wednesday
(submit these on Canvas or in class):
Fill in the blanks with vocabulary words:
- 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*. - 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*.

- Suppose that a function
- Exercises from the textbook due on September 20 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, 3.3.25, 3.3.27, 3.3.29, 3.3.31, 3.3.49, 3.3.51.

- 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 September 20 Friday (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 Monday (submit these through MyLab): 3.6.5, 3.6.13, 3.6.15, 3.6.21, 3.6.23.

- Reading:
- Linear functions:
- Reading: Section 4.1 (pages 281–287) from the textbook.
- Exercises due on September 23 Monday (submit these on Canvas or in class):
- 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*. - Suppose that
*f*is a linear function. If you know*f*(*x*_{1}) and*f*(*x*_{2}) for two distinct real numbers*x*_{1}and*x*_{2}, then give a formula for the slope of the graph of*f*using*x*_{1},*x*_{2},*f*(*x*_{1}), and/or*f*(*x*_{2}).

- Suppose that
- Exercises from the textbook due on September 25 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.

- The library of functions:
- Reading: Section 3.4 Objective 1 (pages 242–246) from the textbook.
- Exercises due on September 25 Wednesday
(submit these on Canvas or in class):
- In the _____ function, the output is always defined and equal to the input.
- 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 September 27 Friday (submit these 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.

- 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 September 27 Friday (submit these on Canvas or in class):
Fill in the blanks with vocabulary words:
- A _____-defined function is defined by a formula together with a condition restricting its inputs.
- A _____-defined function is defined by more than one formula, each with a condition restricting its inputs.

- Exercises from the textbook due on September 30 Monday (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.

- Reading:
- Composite functions:
- Reading:
- Section 6.1 (pages 415–419) from the textbook;
- My online notes on composite functions.

- Exercises due on September 30 Monday (submit these on Canvas or in class):
- 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*) = _____. - 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*.

- Fill in the blanks
with a vocabulary word and a mathematical expression:
If
- Exercises from the textbook due on October 2 Wednesday (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.

- Reading:
- Inverse functions:
- Reading:
- Section 6.2 (pages 423–430) from the textbook;
- My online notes on inverse functions.

- Exercises due on October 2 Wednesday (submit these on Canvas or in class):
- 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.
- Fill in the blank with a vocabulary word:
If
*f*is a one-to-one function, then its _____ function, denoted*f*^{−1}, exists. - 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}. - 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 4 Friday (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, 6.2.35, 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.

- Reading:
- Coordinate transformations:
- Reading:
- Section 3.5 (pages 254–263) from the textbook;
- My online notes on linear coordinate transformations.

- Exercises due on October 4 Friday (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).- 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. - 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*? - To change the graph of
*y*=*f*(*x*) into the graph of*y*=*f*(2*x*), do you*compress*or*stretch*the graph left and right?

- Fill in the blank with a direction:
To change the graph of
- Exercises from the textbook due on October 7 Monday (submit these 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.

- Reading:

- Exponential functions:
- Reading:
- Section 6.3 (pages 435–446) from the textbook;
- My online notes on exponential functions.

- Exercises due on October 7 Monday (submit these on Canvas or in class):
Let
*f*(*x*) be*C**b*^{x}for all*x*.- What is
*f*(*x*+ 1)/*f*(*x*)? - What are
*f*(−1),*f*(0), and*f*(1)?

*b*and/or*C*, and simplify them as much as possible.) - What is
- Exercises from the textbook due on October 9 Wednesday (submit these 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.

- Reading:
- 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 October 9 Wednesday (submit these on Canvas or in class):
Suppose that
*b*> 0 and*b*≠ 1.- Rewrite log
_{b}*M*=*r*as an equation involving exponentiation. - What are
log
_{b}*b*, log_{b}1, and log_{b}(1/*b*)?

- Rewrite log
- Exercises from the textbook due on October 11 Friday (submit these 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.

- Reading:
- 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 October 18 Friday (submit these on Canvas or in class):
Given
*b*> 0,*b*≠ 1, and*u*> 0, write log_{b}*u*in these two ways:- Using only common logarithms (logarithms base 10);
- Using only natural logarithms (logarithms base e).

- Exercises from the textbook due on October 21 Monday (submit these 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.

- Reading:
- Logarithmic expressions:
- 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 October 21 Monday (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.)- log
_{b}(*u**v*) = ___; - log
_{b}(*u*/*v*) = ___; - log
_{b}(*u*^{x}) = ___.

- log
- Exercises from the textbook due on October 23 Wednesday (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.

- Reading:
- Logarithmic equations:
- Reading: Section 6.6 through Objective 2 (pages 474–477) from the textbook.
- Exercises due on October 23 Wednesday (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.)
- log
_{2}(*x*+ 3) = 5; - (
*x*+ 3)^{2}= 5; - 2
^{x+3}= 5.

- log
- Exercises from the textbook due on October 25 Friday (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.

- Compound interest:
- Reading:
- Section 6.7 (pages 481–487) from the textbook;
- My online notes on compound interest.

- Exercises due on October 25 Friday (submit these on Canvas or in class):
- The original amount of money that earns interest is the _____.
- If you borrow
*P*dollars at 100*r*% 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 October 28 Monday (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.

- Reading:
- Applications of logarithms:
- Reading:
- Section 6.8 (pages 478–485) from the textbook;
- My online notes on applications of logarithms.

- Exercises due on October 28 Monday (submit these 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*A*_{0}at time*t*= 0. Write down a formula for the value of*A*as a function of the time*t*. - Suppose that a quantity
*A*undergoes exponential decay with a halflife of*h*and an initial value of*A*_{0}at time*t*= 0. Write down a formula for the value of*A*as a function of the time*t*.

- Suppose that a quantity
- Exercises from the textbook due on October 30 Wednesday (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.

- Reading:

- Quadratic functions:
- Reading:
- Section 4.3 (pages 299–308) from the textbook;
- My online notes on quadratic functions.

- Exercises due on October 30 Wednesday (submit these on Canvas or in class):
- Fill in the blank with a vocabulary word: The shape of the graph of a nonlinear quadratic function is a(n) _____.
- Fill in the blanks with algebraic expressions:
Given
*a*≠ 0 and*f*(*x*) =*a**x*^{2}+*b**x*+*c*for all*x*, the vertex of the graph of*f*is (___, ___). - Given
*a*≠ 0,*b*^{2}− 4*a**c*> 0, and*f*(*x*) =*a**x*^{2}+*b**x*+*c*for all*x*, how many*x*-intercepts does the graph of*y*=*f*(*x*) have?

- Exercises from the textbook due on November 1 Friday (submit these 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.

- Reading:
- Applications of quadratic functions:
- Reading:
- Section 4.4 through Objective 1 (pages 312–316) from the textbook;
- My online notes on economic applications.

- Exercises due on November 6 Wednesday (submit these on Canvas or in class):
- Suppose that
*x*and*y*are variables,*x*can take any value, and*y*=*a**x*^{2}+*b**x*+*c*for some constants*a*,*b*, and*c*.- Fill in the blank with an algebraic equation or inequality:
*y*has a maximum value if _____. - Fill in the blank with an algebraic expression:
In this case,
*y*has its maximum when*x*= ___.

- Fill in the blank with an algebraic equation or inequality:
- If the width of a rectangle is
*w*metres and its length is*l*metres, then what is its area (in square metres)? - 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)? - 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)?

- Suppose that
- Exercises from the textbook due on November 8 Friday (submit these through MyLab): 4.3.87, 4.3.89, 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.

- Reading:
- Power functions:
- Reading:
- My online notes on power functions;
- Section 5.1 through Objective 2 (pages 331–336) from the textbook.

- Exercises due on November 8 Friday (submit these on Canvas or in class):
Give the coordinates of:
- A point on the graph of every power function.
- Another point (different from the answer to #1) on the graph of every power function with a positive exponent.
- Another point on the graph of every power function with an even exponent.
- Another point on the graph of every power function with an odd exponent.

- Exercises from the textbook due on November 11 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.

- Reading:
- 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 through Objective 1 (pages 346–348) from the textbook.

- Exercises due on November 11 Monday (submit these on Canvas or in class):
- 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?
- 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 13 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.

- Reading:
- 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 November 13 Wednesday
(submit these on Canvas or in class):
- 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? - 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*)?

- Suppose that
- Exercises from the textbook due on November 15 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.

- Reading:
- Imaginary roots:
- Reading: Section 5.7 (pages 401–406) from the textbook.
- Exercises due on November 15 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 imaginary complex number*a*+*b*i is a root (aka zero) of*f*.- What other complex number must be a root of
*f*? - What non-constant polynomial in
*x*(with*real*coefficients) must be a factor of*f*(*x*)?

- What other complex number must be a root of
- Exercises from the textbook due on November 18 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.

- Exercises due on November 15 Friday (submit these on Canvas or in class):
Suppose that
- Rational functions and asymptotes:
- Reading:
- Section 5.3 (pages 354–361) from the textbook;
- My online notes on rational functions.

- Exercises due on November 18 Monday (submit these on Canvas or in class):
- 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.
- 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 20 Wednesday (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.

- Reading:
- Graphs of rational functions:
- Reading: Section 5.4 (pages 365–375) from the textbook.
- Exercises due on November 20 Wednesday
(submit these on Canvas or in class):
- 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.
- 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 its non-vertcial linear asymptote. (Warning: Don't mix up lowercase and uppercase letters in your answer!)

- Exercises from the textbook due on November 22 Friday (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.

- Inequalities:
- Reading:
- Section 5.5 (pages 380–384) from the textbook;
- My online notes on solving inequalities.

- Exercises due on November 22 Friday (submit these on Canvas or in class):
Suppose that you have
a rational inequality in the variable
*x*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 two sides 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, 0, or 2.

- Exercises from the textbook due on November 25 Monday (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.

- Reading:

- Graphs and functions:
- Review date: September 13 Friday.
- Date taken: September 16 Monday.
- Corresponding problem sets: 1–8.
- Help allowed: Your notes, calculator.
- NOT allowed: Textbook, my notes, other people, websites, etc.

- Properties and types of functions:
- Review date: October 11 Friday.
- Date taken: October 16 Wednesday.
- Corresponding problem sets: 9–17.
- Help allowed: Your notes, calculator.
- NOT allowed: Textbook, my notes, other people, websites, etc.

- Exponential and logarithmic functions:
- Review date: November 1 Friday.
- Date taken: November 4 Monday.
- Corresponding problem sets: 18–24.
- Help allowed: Your notes, calculator.
- NOT allowed: Textbook, my notes, other people, websites, etc.

- Polynomial and rational functions:
- Review date: November 25 Monday.
- Date taken: December 2 Monday.
- Corresponding problem sets: 25–33.
- Help allowed: Your notes, calculator.
- NOT allowed: Textbook, my notes, other people, websites, etc.

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 exam (DjVu).

This web page and the files linked from it (except for the official syllabus) were written by Toby Bartels, last edited on 2024 October 7. Toby reserves no legal rights to them.

The permanent URI of this web page
is
`https://tobybartels.name/MATH-1150/2024FA/`

.