Here is material about the administration of the course:

- Canvas page (where you must log in for full access, available while the course is in session).
- Help with DjVu (if you have trouble reading the files below).
- Course policies (DjVu).
- Class hours: Mondays and Wednesdays from 5:30 PM to 6:50 in LNK U-105 or online over Zoom.

- Name: Toby Bartels, PhD;
- Canvas messages.
- Email: TBartels@Southeast.edu.
- Voice mail: 1-402-323-3452.
- Text messages: 1-402-805-3021.
- Office hours:
- Mondays and Wednesdays from 9:30 to 10:30,
- Tuesdays and Thursdays from 2:30 PM to 4:00, and
- by appointment,

- General review:
- Date due: January 15 Wednesday.
- Reading:
- My online introduction;
- Skim Chapter R (
*except*Section R.6) and Chapter 1 (*except*Section 1.6) and review anything that you are shaky on.

- Exercises due:
- Which of the following are
*equations*?- 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*= 1 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 January 22 Wednesday on 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.

- Graphing points:
- Date due: January 22 Wednesday.
- Reading: Section 2.1 (pages 150–154) from the textbook.
- Exercises due:
- 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 blank with a number: If the legs of a right triangle have lengths 3 and 4, then the length of its hypotenuse is ___.
- 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 (___, ___).

- Exercises from the textbook due January 27 Monday on 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.

- Graphing equations:
- Date due: January 27 Monday.
- Reading:
- Section 2.2 (pages 157–164) from the textbook;
- My online notes on symmetry and intercepts.

- Exercises due: Fill in the blanks with vocabulary words:
- 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.
- 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 January 29 Wednesday on 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.

- Lines:
- Date due: January 29 Wednesday.
- Reading:
- Section 2.3 (pages 169–179);
- My online notes on lines.

- Exercises due: Fill in the blanks with words or numbers:
- The slope of a vertical line is _____, and the slope of a horizontal line is _____.
- 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 ___.

- Exercises from the textbook due February 3 Monday on 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.

- Systems of equations:
- Date due: February 3 Monday.
- Reading:
- Section 12.1 (pages 868–878);
- My online notes and video on systems of equations.

- Exercises due:
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
- Exercises from the textbook due February 5 Wednesday on MyLab: 12.1.3, 12.1.4, 12.1.6, 12.1.11, 12.1.19, 12.1.21, 12.1.27, 12.1.31, 12.1.45, 12.1.47, 12.1.65, 12.1.73.

- Functions:
- Date due: February 5 Wednesday.
- Reading:
- Section 3.1 (pages 203–215);
- My online notes on functions.

- Exercises due:
- Fill in the blanks with vocabulary words:
If
*f*(3) = 5, then 3 belongs to the _____ of the function, and 5 belongs to its _____. - 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 blanks with vocabulary words:
If
- Exercises from the textbook due February 10 Monday on MyLab: 3.1.1, 3.1.2, 3.1.3, 3.1.10, 3.1.31, 3.1.33, 3.1.35, 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.

- Graphs of functions:
- Date due: February 10 Monday.
- Reading: Most of Section 3.2 (pages 219–223), but you may skip parts D and E of Example 4.
- Exercises due:
- 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.
- True or false:
The graph of a function can have any number of
*x*-intercepts. - True or false:
The graph of a function
can have any number of
*y*-intercepts.

- Fill in the blanks with mathematical expressions:
If (3, 5) is a point on the graph of a function
- Exercises from the textbook due February 12 Wednesday on 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.

- Properties of functions:
- Date due: February 12 Wednesday.
- Reading:
- Section 3.3 (pages 229–237);
- My online notes on properties of functions.

- Exercises due: 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 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
- Exercises from the textbook due February 19 Wednesday on MyLab: 3.3.2, 3.3.3, 3.3.5, 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, 3.3.37, 3.3.39, 3.3.41, 3.3.43, 3.3.45, 3.3.49, 3.3.51.

- Word problems with functions:
- Date due: February 19 Wednesday.
- Reading:
- Most of Section 3.6 (pages 267–269), but you may skip the parts involving graphing calculators;
- My online notes and video on functions in word problems;
- Section 4.1 (pages 281–287).

- Exercises due:
- 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.) - 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 you have a problem with three quantities,
- Exercises from the textbook due February 24 Monday on MyLab: 3.6.5, 3.6.13, 3.6.15, 3.6.17, 3.6.21, 3.6.23, 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.

- Examples of functions:
- Date due: February 24 Monday.
- Reading:
- Section 3.4 Objective 1 (pages 242–246);
- My online notes and video on partially-defined functions;
- The rest of Section 3.4 (pages 247–249).

- Exercises due: Fill in the blanks with vocabulary words:
- In the _____ function, the output is always defined and equal to the input.
- 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 February 26 Wednesday on MyLab: 3.4.9, 3.4.10, 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, 3.4.27, 3.4.29, 3.4.31, 3.4.33, 3.4.35, 3.4.43, 3.4.45, 3.4.51.

- Composite functions:
- Date due: February 26 Wednesday.
- Reading:
- Most of Section 6.1 (pages 415–419);
- My online notes on composite functions.

- Exercise due:
Fill in the blanks with a vocabulary word and a mathematical formula:
If
*f*and*g*are functions, then their _____ function, denoted*f*∘*g*, is defined by (*f*∘*g*)(*x*) = _____. - Exercises from the textbook due March 2 Monday on 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.

- Inverse functions:
- Date due: March 2 Monday.
- Reading:
- Most of Section 6.1: from page 403 to the top of page 407;
- Section 6.2 (pages 423–430);
- My online notes on inverse functions.

- Exercises due:
- 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}.

- Exercises from the textbook due March 4 Wednesday on 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.

- Coordinate transformations:
- Date due: March 4 Wednesday.
- Reading:
- Section 3.5 (pages 254–263);
- My online notes on linear coordinate transformations.

- Exercises due:
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 March 9 Monday on 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.

- Quadratic functions:
- Date due: March 9 Monday.
- Reading:
- Section 4.3 (pages 299–308);
- My online notes on quadratic functions.

- Exercises due:
- 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 March 11 Wednesday on 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.

- Applications of quadratic functions:
- Date due: March 11 Wednesday.
- Reading:
- Section 4.4 through Objective 1 (pages 312–316);
- My online notes on economic applications.

- Exercises due:
- 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)? - 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
- Exercises from the textbook due March 16 Monday on 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.

- Exponential functions:
- Date due: March 16 Monday.
- Reading:
- Section 6.3 (pages 435–446);
- My online notes on exponential functions.

- Exercises due:
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)? (Write your answers using*b*and*C*, and simplify them as much as possible.)

- What is
- Exercises from the textbook due March 30 Monday on 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.

- Logarithmic functions:
- Date due: March 30 Monday.
- Reading:
- Section 6.4 (pages 452–460);
- My online notes on logarithmic functions.

- Exercises due: 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 April 1 Wednesday on 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.

- Properties of logarithms:
- Date due: April 1 Wednesday.
- Reading:
- Section 6.5 (pages 465–471);
- My online notes on laws of logarithms;
- Section 6.6 (pages 474–478).

- Exercises due:
- 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
- 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

- Fill in the blanks
to break down these expressions using properties of logarithms.
(Assume that
- Exercises from the textbook due April 6 Monday on 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, 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.

- Applications of logarithms:
- Date due: April 6 Monday.
- Reading:
- Section 6.7 (pages 481–487);
- Section 6.8: pages 478–485;
- My online notes on applications of logarithms.

- Exercises due:
- The original amount of money that earns interest is the _____.
- 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*.

- Exercises from the textbook due April 8 Wednesday on 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, 6.8.1, 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 functions:
- Date due: April 8 Wednesday.
- Reading:
- Section 5.1 (pages 331–342);
- My online notes on graphing polynomials (but the last paragraph is optional);
- Section 5.2 Objective 1 (pages 346–348).

- Exercises due:
- Give the coordinates of a point on the graph of every power function, another point (different from the previous point) on the graph of every power function with a positive exponent, another point on the graph of every power function with an even exponent, and another point on the graph of every power function with an odd exponent.
- If a root (zero) of a polynomial function has odd multiplicity, 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?

- Exercises from the textbook due April 13 Monday on MyLab: 5.1.1, 5.1.2, 5.1.11, 5.1.15, 5.1.17, 5.1.19, 5.1.21, 5.1.27, 5.1.29, 5.1.33, 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.

- Advanced factoring:
- Date due: April 13 Monday.
- Reading:
- Section R.6 (pages 57–60);
- Section 5.6 through Objective 1 (pages 387–390);
- Section 5.6 Objectives 3–5 (pages 391–395).

- Exercises due:
- 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
*f*is a polynomial function with real coefficients and*a*and*b*are real numbers with*b*≠ 0. If the imaginary complex number*a*+*b*i is a root (or zero) of*f*, then what other number must be a root of*f*?

- Suppose that
- Exercises from the textbook due April 15 Wednesday on 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, 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.

- Rational functions:
- Date due: April 15 Wednesday.
- Reading:
- Section 5.3 (pages 354–361);
- Section 5.4 (pages 365–375);
- My online notes on rational functions.

- Exercises due:
- 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.
- 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.

- Exercises from the textbook due April 20 Monday on 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, 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:
- Date due: April 20 Monday.
- Reading:
- Section 5.5 (pages 380–384);
- My online notes on solving inequalities.

- Exercise due:
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, 0, or 2.

- Exercises from the textbook due April 22 Wednesday on 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.

This web page and the files linked from it were written by Toby Bartels, last edited on 2021 January 11. Toby reserves no legal rights to them.

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