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: July 10 Monday.
   • Date due: July 12 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.
   • Problems 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: July 12 Wednesday.
   • Date due: July 17 Monday.
   • Reading:
     • Section 2.1 (pages 150–154);
     • Section 2.2 (pages 157–164);
     • My online notes on symmetry and intercepts.
   • Problems due:
     • From §2.1 (page 154): 2, 3, 8;
     • From §2.2 (page 164): 3, 5.
3. Linear equations:
   • Date assigned: July 17 Monday.
   • Date due: July 19 Wednesday.
   • 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.
   • Problems due:
     • From §2.3 (page 178): 1, 7, 8;
     • From §12.1 (page 854): 3, 5.
4. Functions:
   • Date assigned: July 19 Wednesday.
   • Date due: July 24 Monday.
   • 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.
   • Problems due:
     • From §3.1 (page 210): 9, 10, 15;
     • From §3.2 (page 218): 3, 4, 10.
5. Properties of functions:
   • Date assigned: July 24 Monday.
   • Date due: July 26 Wednesday.
   • 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.
   • Problems 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: July 26 Wednesday.
   • Date due: July 31 Monday.
   • 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.
   • Problem 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: July 31 Monday.
   • Date due: August 2 Wednesday.
   • 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).
   • Problems 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: August 2 Wednesday.
   • Date due: August 7 Monday.
   • 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.
   • Problems due:
     • From §6.1 (pages 408–410): 4, 6.
     • From §6.2 (pages 419–423): 6, 11.
9. Coordinate transformations:
   • Date assigned: August 7 Monday.
   • Date due: August 9 Wednesday.
   • Reading:
     • Section 3.5 (pages 247–256);
     • My online notes on linear coordinate transformations.
   • Problems due from §3.5 (pages 256–260): 1, 2.
10. Quadratic functions:
    • Date assigned: August 9 Wednesday.
    • Date due: August 14 Monday.
    • 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.
    • Problems 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: August 14 Monday.
    • Date due: August 16 Wednesday.
    • Reading:
      • Section 6.3 (pages 423–434);
      • Section 6.4 (pages 440–448);
      • My online notes on exponential and logarithmic functions.
    • Problems due:
      • From §6.3 (pages 434–439): 7, 11;
      • From §6.4 (pages 448–452): 4, 6.
12. Properties of logarithms:
    • Date assigned: August 16 Wednesday.
    • Date due: August 21 Monday.
    • Reading:
      • Section 6.5 (pages 452–458);
      • My online notes on laws of logarithms;
      • Section 6.6: pages 461–464.
    • Problems 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: August 21 Monday.
    • Date due: August 23 Wednesday.
    • Reading:
      • Section 6.7 (pages 468–474);
      • Section 6.8: pages 478–485;
      • My online notes on applications of logarithms.
    • Problems 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: August 23 Wednesday.
    • Date due: August 28 Monday.
    • Reading:
      • Section 5.1 (pages 322–336);
      • My online notes on graphing polynomials (but the last paragraph is optional).
    • Problems due from §5.1 (pages 338–342): 8, 9, 15.
15. Advanced factoring:
    • Date assigned: August 28 Monday.
    • Date due: August 30 Wednesday.
    • 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).
    • Problems due:
      • From §5.5 (pages 386–389): 6, 9.
      • From §5.6 (pages 394&395): 3, 4.
16. Rational functions:
    • Date assigned: August 30 Wednesday.
    • Date due: September 6 Wednesday.
    • Reading:
      • Section 5.2 (pages 343–350);
      • Section 5.3 (pages 353–364);
      • My online notes on rational functions.
    • Problems due:
      • From §5.2 (pages 350–353): 6, 7, 13;
      • From §5.3 (pages 365–368): 3, 6.
17. Inequalities:
    • Date assigned: September 6 Wednesday.
    • Date due: September 11 Monday.
    • Reading:
      • Section 5.4 (pages 368–372);
      • My online notes on solving inequalities.
    • Problems 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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