Readings and homework

Here are the assigned readings and exercises (Reading 1, Reading 2, Reading 3, Reading 4, Reading 5, Reading 6, Reading 7, Reading 8, Reading 9, Reading 10, Reading 11, Reading 12, Reading 13, Reading 14, Reading 15, Reading 16, Reading 17); but anything whose assigned date is in the future is subject to change!

1. Introduction and review:
   • Date assigned: March 28 or 29.
   • Date due: April 2 or 3.
   • 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:
     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.
2. Graphing:
   • Date assigned: April 2 or 3.
   • Date due: April 4 or 5.
   • Reading:
     • Section 2.1 (pages 150–154);
     • Section 2.2 (pages 157–164);
     • My online notes on symmetry and intercepts.
   • Exercises due:
     • From §2.1 (page 154): 2, 3, 8;
     • From §2.2 (page 164): 3, 5.
3. Linear equations:
   • Date assigned: April 4 or 5.
   • Date due: April 9 or 10.
   • Reading:
     • Section 2.3 (pages 167–177);
     • My online notes on lines;
     • Section 12.1 (pages 844–854);
     • My online notes on systems of equations.
   • Exercises due:
     • From §2.3 (page 178): 1, 7, 8;
     • From §12.1 (page 854): 3, 5.
4. Functions:
   • Date assigned: April 9 or 10.
   • Date due: April 11 or 12.
   • Reading:
     • Section 3.1 (pages 199–210);
     • Most of Section 3.2 (pages 214–218), but you may skip parts D and E of Example 4;
     • My online notes on functions.
   • Exercises due:
     • From §3.1 (page 210): 9, 10, 15;
     • From §3.2 (page 218): 3, 4, 10.
5. Properties of functions:
   • Date assigned: April 11 or 12.
   • Date due: April 16 or 17.
   • Reading:
     • Section 3.3 (pages 223–231);
     • The definition of ‘real zero’ on page 327;
     • The definition of ‘linear function’ on page 274;
     • The theorem on rates of change of linear functions on page 275;
     • My online notes on properties of functions.
   • Exercises due:
     • From §3.3 (page 232): 6, 7;
     • Additional problem: Fill in the blank with a vocabulary word: If c is a number and f is a function, and if f(c) = 0, then c is a ___ of f.
6. Word problems:
   • Date assigned: April 16 or 17.
   • Date due: April 18 or 19.
   • Reading:
     • Most of Section 3.6: pages 260–262 (but you may skip the parts about graphing calculators);
     • My online notes on functions in word problems.
   • Exercise 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 any of them.)
7. Examples of functions:
   • Date assigned: April 18 or 19.
   • Date due: April 23 or 24.
   • Reading:
     • Section 4.1 (pages 274–280);
     • Section 3.4, Library of functions (pages 237–241);
     • My online notes on partial functions;
     • Section 3.4, Piecewise-defined functions (pages 242&243).
   • Exercises due:
     • Identify which of the following functions are linear:
       1. f(x) = 3x − 2;
       2. g(x) = 3/x + 2;
       3. h(x) = 3/2.
     • From §3.4 (pages 244–247): 4, 5, 9.
8. Composite and inverse functions:
   • Date assigned: April 23 or 24.
   • Date due: April 25 or 26.
   • Reading:
     • Most of Section 6.1: from page 403 to the top of page 407;
     • Section 6.2 (pages 411–419);
     • My online notes on composite and inverse functions.
   • Exercises due:
     • From §6.1 (pages 408–410): 4, 6.
     • From §6.2 (pages 419–423): 6, 11.
9. Coordinate transformations:
   • Date assigned: April 25 or 26.
   • Date due: April 30 or May 1.
   • Reading:
     • Section 3.5 (pages 247–256);
     • My online notes on linear coordinate transformations.
   • Exercises due from §3.5 (pages 256–260): 1, 2.
10. Quadratic functions:
    • Date assigned: April 30 or May 1.
    • Date due: May 2 or 3.
    • Reading:
      • Section 4.3 (pages 291–298);
      • My online notes on quadratic functions;
      • Most of Section 4.4: from page 302 through the top half of page 306;
      • My online notes on economic applications.
    • Exercises due:
      • From §4.3 (pages 299–302): 5, 7, 11;
      • Additional problem: 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)?
11. Exponential and logarithmic functions:
    • Date assigned: May 2 or 3.
    • Date due: May 7 or 8.
    • Reading:
      • Section 6.3 (pages 423–434);
      • Section 6.4 (pages 440–448);
      • My online notes on exponential and logarithmic functions.
    • Exercises due:
      • From §6.3 (pages 434–439): 7, 11;
      • From §6.4 (pages 448–452): 4, 6.
12. Properties of logarithms:
    • Date assigned: May 7 or 8.
    • Date due: May 9 or 10.
    • Reading:
      • Section 6.5 (pages 452–458);
      • My online notes on laws of logarithms;
      • Section 6.6: pages 461–464.
    • Exercises due:
      • From §6.5 (pages 459&460): 1–6.
      • Additional problem: 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?
        1. log₂ (x + 3) = 5;
        2. (x + 3)² = 5;
        3. 2^{x + 3} = 5.
13. Applications of logarithms:
    • Date assigned: May 9 or 10.
    • Date due: May 14 or 15.
    • Reading:
      • Section 6.7 (pages 468–474);
      • Section 6.8: pages 478–485;
      • My online notes on applications of logarithms.
    • Exercises due:
      • From §6.7 (pages 474–477): 3, 5;
      • Addtional problem: 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.
14. Polynomial functions:
    • Date assigned: May 14 or 15.
    • Date due: May 16 or 17.
    • Reading:
      • Section 5.1 (pages 322–336);
      • My online notes on graphing polynomials (but the last paragraph is optional).
    • Exercises due from §5.1 (pages 338–342): 8, 9, 15.
15. Advanced factoring:
    • Date assigned: May 16 or 17.
    • Date due: May 21 or 22.
    • Reading:
      • Section R.6 (pages 58–61);
      • from Section 5.5:
        • the introduction and subsection 1 (from page 375 through the middle of page 378),
        • subsections 3–5 (from the middle of page 379 to the top of page 383).
      • Section 5.6 (pages 390–394).
    • Exercises due:
      • From §5.5 (pages 386–389): 6, 9.
      • From §5.6 (pages 394&395): 3, 4.
16. Rational functions:
    • Date assigned: May 21 or 22.
    • Date due: May 23 or 24.
    • Reading:
      • Section 5.2 (pages 343–350);
      • Section 5.3 (pages 353–364);
      • My online notes on rational functions.
    • Exercises due:
      • From §5.2 (pages 350–353): 6, 7, 13;
      • From §5.3 (pages 365–368): 3, 6.
17. Inequalities:
    • Date assigned: May 23 or 24.
    • Date due: May 30 or 29.
    • Reading:
      • Section 5.4 (pages 368–372);
      • My online notes on solving inequalities.
    • Exercises due:
      • From §5.4 (pages 372–375): 3;
      • Additional problem: 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:
        1. the left-hand side is always defined;
        2. the right-hand side is undefined when x is 2 but is otherwise defined;
        3. the left-hand side and right-hand side are equal when x is −3/2 and only then;
        4. the original inequality is true when x is −3/2 or 3 but false when x is −2, 0, or 2.
        What are the solutions to the inequality?

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