MATH-1100-LN03

Course administration

• Canvas page (where you must log in).
• Help with DjVu (if you have trouble reading the DjVu files on this page).
• SCC syllabus (DjVu).
• SCC Course Statements.
• SCC Student Technical Support Resources (DjVu).
• My course policies (DjVu).
• Class hours: Mondays, Wednesdays, and Fridays from 11:00 to 11:50 in room U6.
• Final exam time: December 8 Monday from 11:00 to 12:40 in room U6 (or by appointment).

Contact information

• Name: Toby Bartels, PhD.
• Canvas messages.
• Email: TBartels@Southeast.edu.
• Voice mail: 1-402-323-3452.
• Text messages: 1-402-805-3021.
• Office hours: Weekdays from 10:00 to 10:50 (or by appointment) in room U9C (or over Zoom meeting 610-024-2876).

Readings

Try to read this introduction before the first day of class:

• Objectives:
  • Understand what to expect from this course;
  • Know how to submit assignments.
• Reading:
  • The course policies (DjVu, same as above).
  • Section 1.1 (pages 1–7) from the textbook.
• Problem set from the textbook due on August 20 Wednesday or ASAP thereafter (submit this 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.

Roots and radicals

1. General review:
   • Objectives:
     • Review multiplying polynomials;
     • Review factoring techniques;
     • Review solving equations by factoring.
   • Reading from (mostly) the textbook:
     • Skim Chapter 6 (pages 368–431) from the textbook, and review anything that you don't remember well;
     • Optional: My online factoring review.
   • Reading homework due on August 20 Wednesday (submit this in class or on Canvas):
     1. Fill in the blank with a plural vocabulary word: In the product (3x − 2)(x + 4) = 3x² + 10x − 8, the polynomials 3x − 2 and x + 4 are the _____ of the polynomial 3x² + 10x − 8.
     2. Which is the correct solution to 6 − 2x < 0?
        1. x < 3, or equivalently x ∈ (−∞, 3);
        2. x ≤ 3, or equivalently x ∈ (−∞, 3];
        3. x > 3, or equivalently x ∈ (3, ∞);
        4. x ≥ 3, or equivalently x ∈ [3, ∞).
     3. Fill in the blanks with simpler equations: If AB = 0, then _____ or _____.
   • Problem set from the textbook due on August 22 Friday (submit this through MyLab): 2.2.75, 5.3.53, 5.5.13, 6.1.95, 6.2.47, 6.4.45.
2. Roots:
   • Objectives:
     • Define real roots with odd indices;
     • Define principal roots with even indices;
     • Identify when a root is defined in the real-number system;
     • Evaluate rational roots of rational numbers.
   • Reading from (mostly) the textbook:
     • Skim: Section 9.1 (pages 616–619);
     • Section 9.2 through Objective 2 (pages 620–623);
     • My notes on roots.
   • Reading homework due on August 22 Friday (submit this in class or on Canvas):
     1. In the expression ⁿ√b, the real number b is the _____, and the natural number n is the _____.
     2. Under which of the following conditions is ⁿ√b (the principal real nth root of b) defined (as a real number)? Answer Yes or No for each.
        1. When n is even and b is positive;
        2. When n is even and b is negative;
        3. When n is odd and b is positive;
        4. When n is odd and b is negative.
   • Problem set from the textbook due on August 25 Monday (submit this through MyLab): 9.1.33, 9.1.35, 9.1.37, 9.2.37, 9.2.39, 9.2.41, 9.2.43, 9.2.45, 9.2.47, 9.2.49, 9.2.51, 9.2.101, 9.2.103, 9.2.105, 9.2.111.
3. Fractional exponents:
   • Objectives:
     • Convert an expression with a rational exponent to one with a power and/or a root;
     • Evaluate rational powers of rational numbers with rational exponents;
     • Test alleged rules of exponentiation.
   • Reading from the textbook:
     • The rest of Section 9.2 (pages 623–626);
     • Section 9.3 (pages 628–632);
     • Warning: Some of the rules listed on page 629 under "The Laws of Exponents" are not correct as stated, where a and b can be any real numbers and r and s can be any rational numbers. It's safer to learn these rules only when a and b are both positive (or r and s are both integers). In the next reading, I'll give some rules that you can safely use in all situations involving real numbers, expressed using radicals instead of fractional exponents.
   • Reading homework due on August 25 Monday (submit this in class or on Canvas):
     1. Write ⁿ√b using a fractional exponent.
     2. Assuming that m/‍n is a rational number in lowest terms, write b^m/‍n using only roots and powers with integer exponents.
     3. Consider the Power Rule as stated on page 629 of the textbook: (a^r)^s = a^r⋅s, where a is a real number and r and s are rational numbers. Check this rule when a is −1, r is 2, and s is ½; what do you get for the left-hand side and the right-hand side in this example? Is the rule correct in this case?
   • Problem set from the textbook due on August 27 Wednesday (submit this through MyLab): 9.2.73, 9.2.75, 9.2.93, 9.2.95, 9.2.97, 9.2.99, 9.2.109, 9.2.113, 9.4.37, 9.4.39, 9.4.133, 9.3.69, 9.3.71, 9.3.75.
4. Simplifying radical expressions:
   • Objectives:
     • Simplify a root of a power;
     • Simplify a root when the radicand has a power as a factor;
     • Simplify a root of a power when the index and exponent don't match;
     • Simplify a root of a root;
     • Know when absolute values can be removed.
   • Reading from (mostly) the textbook:
     • My notes on simplifying roots;
     • Section 9.4 (pages 634–641).
   • Reading homework due on August 27 Wednesday (submit this in class or on Canvas):
     1. Simplify √x² without using roots or fractional exponents and without making any assumptions about x (besides that it's a real number).
     2. Assuming that ⁿ√a ⁿ√b exists (as a real number), express it as a single root.
     3. Assuming that ^m√ⁿ√b exists (as a real number), express it as a single root.
   • Problem set from the textbook due on August 29 Friday (submit this through MyLab): 9.2.53, 9.2.55, 9.2.57, 9.2.107, 9.4.41, 9.4.43, 9.4.45, 9.4.47, 9.4.49, 9.4.119, 9.4.121, 9.4.123, 9.4.125, 9.4.127, 9.4.129, 9.4.131, 9.3.65, 9.3.87.
5. Adding and subtracting radical expressions:
   • Objectives:
     • Identify like terms in a radical expression;
     • Add radical expressions;
     • Take the opposite of a radical expression;
     • Subtract radical expressions.
   • Reading from the textbook: Section 9.5 through Objective 1 (pages 643–645).
   • Reading homework due on August 29 Friday (submit this in class or on Canvas):
     1. As 2x + 3x = 5x, so 2√7 + 3√7 = _____.
     2. As (x + 2)(x + 3) = x² + 5x + 6, so (∛7 + 2)(∛7 + 3) = _____. (Remember that (∛7)² = ∛49.)
   • Problem set from the textbook due on September 3 Wednesday (submit this through MyLab): 9.5.19, 9.5.21, 9.5.23, 9.5.25, 9.5.27, 9.5.29, 9.5.31, 9.5.33, 9.5.41.

More radicals

6. Multiplying radical expressions:
   • Objectives:
     • Multiply roots;
     • Raise a root to a power;
     • Multiply radical expressions;
     • Raise a radical expression to a power.
   • Reading from the textbook: The rest of Section 9.5 (pages 645–647).
   • Reading homework due on September 3 Wednesday (submit this in class or on Canvas):
     1. While x² doesn't simplify, (√x)² = _____.
     2. As (x + 2)(x + 3) = x² + 5x + 6, so (√x + 2)(√x + 3) = _____. (Use the previous result to simplify.)
   • Problem set from the textbook due on September 5 Friday (submit this through MyLab): 9.5.49, 9.5.51, 9.5.53, 9.5.55, 9.5.57, 9.5.63, 9.5.65, 9.5.67, 9.5.69, 9.5.71, 9.5.75, 9.5.109.
7. Dividing radical expressions:
   • Objectives:
     • Rationalize a denominator that's a root;
     • Rationalize a denominator with two terms, one rational and one a square root;
     • Rationalize a denominator with two terms, each a square root;
     • Take the reciprocal of a radical expression;
     • Divide radical expressions.
   • Reading from the textbook: Section 9.6 (pages 649–653).
   • Reading homework due on September 5 Friday (submit this in class or on Canvas):
     1. To rationalize the denominator of a/‍√b, multiply top and bottom by _____.
     2. To rationalize the denominator of a/‍∛b, multiply top and bottom by _____.
     3. To rationalize the denominator of a/‍∛b², multiply top and bottom by _____.
     4. To rationalize the denominator of a/‍(√b + c), multiply top and bottom by _____.
   • Problem set from the textbook due on September 10 Wednesday (submit this through MyLab): 9.6.13, 9.6.15, 9.6.17, 9.6.19, 9.6.21, 9.6.23, 9.6.25, 9.6.27, 9.6.29, 9.6.31, 9.6.33, 9.6.37, 9.6.41, 9.6.47, 9.6.51, 9.6.61.
8. Radical equations:
   • Objectives:
     • Isolate the root in a radical equation;
     • Solve radical equations with odd-indexed roots;
     • Solve radical equations with even-indexed roots;
     • Solve radical equations with multiple roots.
   • Reading from the textbook: Section 9.8 (pages 662–667).
   • Reading homework due on September 10 Wednesday (submit this in class or on Canvas):
     1. Fill in the blank with an appropriate term: A _____ equation is an equation where one or both sides are radical expressions.
     2. True or false: After solving a radical equation, even if you're sure that you didn't make any mistakes, you generally still need to check your solutions.
     3. Fill in the blank with an equation that doesn't involve radicals (or fractional exponents): If a ≥ 0, then √u = a is equivalent to _____.
   • Problem set from the textbook due on September 12 Friday (submit this through MyLab): 9.8.17, 9.8.19, 9.8.23, 9.8.33, 9.8.39, 9.8.43, 9.8.47, 9.8.51, 9.8.55, 9.8.57, 9.8.61, 9.8.105.
9. Complex numbers:
   • Objectives:
     • Graph a complex number on the complex-number plane;
     • Take the principal square root of a negative number;
     • Add complex numbers;
     • Subtract complex numbers;
     • Multiply complex numbers.
   • Reading from the textbook: Section 9.9 through Objective 3 (pages 670–676).
   • Reading homework due on September 12 Friday (submit this in class or on Canvas):
     1. Fill in the blank with a number: i² = ___ (where i is the imaginary unit).
     2. Fill in the blank with an algebraic expression: If a is a positive real number, then √−a = ___. (Write this so that the expression doesn't include any root operations whose outputs are imaginary.)
     3. True or false: Every real number is also a complex number.
   • Problem set from the textbook due on September 15 Monday (submit this through MyLab): 9.9.25, 9.9.27, 9.9.29, 9.9.33, 9.9.35, 9.9.37, 9.9.39, 9.9.41, 9.9.43, 9.9.45, 9.9.51, 9.9.53, 9.9.55, 9.9.57.
10. Advanced operations on complex numbers:
    • Objectives:
      • Take the complex conjugate of a complex number;
      • Take the absolute value of a complex number;
      • Take the reciprocal of a complex number;
      • Divide complex numbers;
      • Raise a complex number to a power.
    • Reading from the textbook: The rest of Section 9.9 (pages 676–678).
    • Reading homework due on September 15 Monday (submit this in class or on Canvas): Suppose that a and b are real numbers.
      1. What is the complex conjugate of a + bi?
      2. Write the reciprocal of a + bi with only real denominators.
    • Problem set from the textbook due on September 17 Wednesday (submit this through MyLab): 9.9.81, 9.9.83, 9.9.85, 9.9.87, 9.9.89, 9.9.95, 9.9.97, 9.9.99, 9.9.101, 9.9.141.

Quadratic equations

11. Basic quadratic equations:
    • Objectives:
      • Identify quadratic equations;
      • Check complex solutions of a real quadratic equation;
      • Solve a quadratic equation in which the variable appears only once.
    • Reading from the textbook: Section 10.1 through Objective 1 (pages 690–694).
    • Reading homework due on September 17 Wednesday (submit this in class or on Canvas):
      1. Solve x² = q² for x.
      2. Assuming that c ≠ 0, solve x² = c for x in the complex-number system.
    • Problem set from the textbook due on September 19 Friday (submit this through MyLab): 10.1.19, 10.1.21, 10.1.23, 10.1.25, 10.1.27, 10.1.29, 10.1.31, 10.1.33.
12. Completing the square:
    • Objectives:
      • Complete the square in a quadratic expression;
      • Solve a quadratic equation by completing the square.
    • Reading from (mostly) the textbook:
      • Section 10.1 Objectives 2&3 (pages 694–697);
      • My notes on solving quadratic equations.
    • Reading homework due on September 19 Friday (submit this in class or on Canvas):
      1. Starting from x² + 2px, what do you add to complete the square?
      2. Starting from x² + bx, what do you add to complete the square?
    • Problem set from the textbook due on September 24 Wednesday (submit this through MyLab): 10.1.45, 10.1.47, 10.1.49, 10.1.51, 10.1.53, 10.1.55, 10.1.57, 10.1.59, 10.1.61, 10.1.63, 10.1.65, 10.1.67.
13. The quadratic formula:
    • Objectives:
      • Solve a quadratic equation using the quadratic formula;
      • Classify solutions of a quadratic equation using its discriminant.
    • Reading from (mostly) the textbook:
      • Section 10.2 through Objective 2 (pages 702–711);
      • My notes on classifying solutions to quadratic equations.
    • Reading homework due on September 24 Wednesday (submit this in class or on Canvas):
      1. Assuming that a ≠ 0, solve ax² + bx + c = 0 for x in the complex-number system.
      2. Fill in the blank with a vocabulary word: The _____ of ax² + bx + c is b² − 4ac.
    • Problem set from the textbook due on September 26 Friday (submit this through MyLab): 10.2.23, 10.2.25, 10.2.27, 10.2.29, 10.2.31, 10.2.33, 10.2.35, 10.2.37, 10.2.39, 10.2.41, 10.2.43, 10.2.45, 10.2.47, 10.2.49.
14. Fancy equations:
    • Objectives:
      • Identify when an equation becomes quadratic upon performing a substitution;
      • Solve such equations.
    • Reading from the textbook: Section 10.3 (pages 716–720).
    • Reading homework due on September 26 Friday (submit this in class or on Canvas):
      1. To turn ∛x² + ∛x = 1 into a quadratic equation, substitute u = ___.
      2. To turn 1/‍x² + 1/‍x = 1 into a quadratic equation, substitute u = ___.
    • Problem set from the textbook due on September 29 Monday (submit this through MyLab): 10.2.71, 10.2.73, 10.2.75, 10.3.49, 10.3.51, 10.3.53, 10.3.55, 10.3.57, 10.3.59.
15. Word problems with quadratic equations:
    • Objectives:
      • Use the Pythagorean Theorem to set up a word problem;
      • Solve a word problem using quadratic equations;
      • Interpret the solutions to a word problem.
    • Reading from the textbook:
      • Section 10.1 Objective 4 (pages 697–699);
      • Section 10.2 Objective 3 (pages 711&712).
    • Reading homework due on September 29 Monday (submit this in class or on Canvas):
      1. Pythagorean Theorem: If a, b, and c are the lengths of the sides of a right triangle, with c the length of the side opposite the right angle, then what equation holds between a, b, and c?
      2. If x² = 4, where x is the length of a road in miles, then what is the length of the road?
    • Problem set from the textbook due on October 1 Wednesday (submit this through MyLab): 10.1.75, 10.1.77, 10.1.83, 10.1.95, 10.1.97, 10.1.99, 10.2.87, 10.2.89, 10.2.93.

Dividing polynomials

16. Rational expressions:
    • Objectives:
      • Identify rational expressions;
      • Evaluate rational expressions;
      • Find when rational expressions are defined;
      • Simplify rational expressions.
    • Reading from (mostly) the textbook:
      • My notes on rational expressions;
      • Section 7.1 (pages 433–439).
    • Reading homework due on October 1 Wednesday (submit this in class or on Canvas):
      1. Fill in the blank with a vocabulary word: A(n) _____ expression is the result of dividing two polynomials.
      2. Fill in the blank with a number (or a kind of number): The result of evaluating a rational expression is undefined if and only if the denominator evaluates to _____.
    • Problem set from the textbook due on October 3 Friday (submit this through MyLab): 7.1.21, 7.1.23, 7.1.25, 7.1.27, 7.1.29, 7.1.31, 7.1.33, 7.1.35, 7.1.37, 7.1.39, 7.1.41, 7.1.43, 7.1.45, 7.1.47, 7.1.49, 7.1.51, 7.1.85.
17. Multiplying and dividing rational expressions:
    • Objectives:
      • Multiply rational expressions;
      • Find the reciprocal of a rational expression;
      • Divide rational expressions.
    • Reading from the textbook: Section 7.2 (pages 441–446).
    • Reading homework due on October 3 Friday (submit this in class or on Canvas):
      1. Fill in the blank with a simplified algebraic expression: (A‍/‍B) ⋅ (C‍/‍D) = _____.
      2. Fill in the blank with a vocabulary word: To divide by a rational expression, multiply by its _____.
    • Problem set from the textbook due on October 8 Wednesday (submit this through MyLab): 7.2.31, 7.2.33, 7.2.35, 7.2.37, 7.2.39, 7.2.41, 7.2.43, 7.2.45, 7.2.47, 7.2.49, 7.2.51.
18. Equivalent rational expressions:
    • Objectives:
      • Find common denominators of rational expressions;
      • Rewrite rational expressions to have common denominators.
    • Reading from the textbook: Section 7.4 (pages 456–460).
    • Reading homework due on October 8 Wednesday (submit this in class or on Canvas):
      1. Fill in the blanks: The _____ _____ _____ of two rational expressions is the lowest-degree polynomial that is a multiple of both of the original expressions' denominators.
      2. What is the least common denominator of 1⁄8 and 5⁄18?
    • Problem set from the textbook due on October 10 Friday (submit this through MyLab): 7.4.13, 7.4.17, 7.4.19, 7.4.23, 7.4.25, 7.4.35, 7.4.39, 7.4.43, 7.4.47, 7.4.51, 7.4.53, 7.4.57, 7.4.69.
19. Adding and subtracting common denominators:
    • Objectives:
      • Add rational expressions with the same denominator;
      • Subtract rational expressions with the same denominator.
    • Reading from the textbook: Section 7.3 (pages 449–453).
    • Reading homework due on October 10 Friday (submit this in class or on Canvas): Which of the following is a correct algebraic rule? (Say Yes or No for each.)
      1. A‍/‍C + B‍/‍C = (A + B)‍/‍C.
      2. A‍/‍C − B‍/‍C = (A − B)‍/‍C.
      3. A‍/‍B + A‍/‍C = A‍/‍(B + C).
      4. A‍/‍B − A‍/‍C = A‍/‍(B − C).
    • Problem set from the textbook due on October 13 Monday (submit this through MyLab): 7.3.17, 7.3.23, 7.3.29, 7.3.31, 7.3.35, 7.3.41, 7.3.43, 7.3.49, 7.3.55, 7.3.61, 7.3.65, 7.3.73, 7.3.89.

More rational expressions

20. Adding and subtracting rational expressions:
    • Objectives:
      • Add rational expressions with different denominators;
      • Subtract rational expressions with different denominators.
    • Reading from the textbook: Section 7.5 (pages 463–470).
    • Reading homework due on October 15 Wednesday (submit this in class or on Canvas): For which of the following operations between rational expressions do you need to get a common denominator? (Say Yes or No for each.)
      1. Addition.
      2. Subtraction.
      3. Multiplication.
      4. Division.
    • Problem set from the textbook due on October 17 Friday (submit this through MyLab): 7.5.45, 7.5.47, 7.5.49, 7.5.51, 7.5.53, 7.5.55, 7.5.57, 7.5.59, 7.5.61, 7.5.63, 7.5.65, 7.5.67, 7.5.95.
21. Complex rational expressions:
    • Objectives:
      • Identify complex rational expressions;
      • Simply complex rational expressions;
      • Compare two methods to simplify complex rational expressions.
    • Reading from the textbook: Section 7.6 (pages 473–478).
    • Reading homework due on October 17 Friday (submit this in class or on Canvas): Fill in the blanks with one word each:
      1. A rational expression with rational subexpressions inside it is called a _____ rational expression.
      2. If you simplify a rational expression by Method I (from Objective 1 on pages 474–476 of the textbook), then you divide the _____ and _____ after simplifying them separately.
      3. If you simplify a rational expression by Method II (from Objective 2 on pages 477&478 of the textbook), then you multiply the numerator and denominator by the _____ _____ _____ of the subexpressions.
    • Problem set from the textbook due on October 22 Wednesday (submit this through MyLab): 7.6.11, 7.6.13, 7.6.25, 7.6.27, 7.6.39, 7.6.41, 7.6.43, 7.6.45, 7.6.47, 7.6.49, 7.6.51.
22. Rational equations:
    • Objectives:
      • Review solving polynomial equations;
      • Identify rational equations;
      • Solve rational equations;
      • Check rational equations for extraneous solutions;
      • Compare two methods to solve rational equations.
    • Reading from (mostly) the textbook:
      • My notes on rational equations;
      • Section 7.7 (pages 481–490);
      • Section 7.8 through the beginning of Objective 1 (pages 493&494).
    • Reading homework due on October 22 Wednesday (submit this in class or on Canvas):
      1. Fill in the blank with an appropriate term: A _____ equation is an equation where both sides are rational expressions.
      2. True or false: After solving a rational equation, even if you're sure that you didn't make any mistakes, you generally still need to check your solutions.
      3. Fill in the blanks with appropriate variables: If A/‍B = C/‍D, then A___ = B___.
    • Problem set from the textbook due on October 24 Friday (submit this through MyLab): 7.7.15, 7.7.17, 7.7.19, 7.7.21, 7.7.23, 7.7.25, 7.7.27, 7.7.29, 7.7.31, 7.7.33, 7.7.47, 7.7.49, 7.7.51, 7.7.53, 7.8.19, 7.8.21, 7.8.29.
23. Word problems with division:
    • Objectives:
      • Set up word problems involving proportions;
      • Set up word problems involving similar triangles;
      • Set up word problems involving rates of work;
      • Set up word problems involving uniform motion;
      • Solve word problems using rational equations once they're set up.
    • Reading from the textbook: The rest of Section 7.8 (pages 494–502).
    • Reading homework due on October 24 Friday (submit this in class or on Canvas):
      1. True or false: If the angles in two geometric figures are equal, then their corresponding lengths are also equal.
      2. True or false: If the angles in two geometric figures are equal, then their corresponding lengths are proportional.
      3. If a job can be completed in 4 hours, then what is the rate at which the job is completed, in jobs per hour?
    • Problem set from the textbook due on October 27 Monday (submit this through MyLab): 7.8.41, 7.8.43, 7.8.45, 7.8.47, 7.8.49, 7.8.51, 7.8.53, 7.8.55, 7.8.57, 7.8.61, 7.8.67, 7.8.69, 7.8.73, 7.8.79.

Inequalities and absolute values

24. Compound inequalities:
    • Objectives:
      • Review linear inequalities;
      • Determine the truth or falsehood of a compound statement from the truth and/or falsehood of the constituent statements;
      • Express the solution set of a compound inequality in interval notation;
      • Solve compound statements by solving the individual statements;
      • Solve linear compound inequalities directly.
    • Reading from (mostly) the textbook:
      • Skim: Section 2.8 (pages 148–157);
      • My notes on inequalities;
      • Section 8.6 through Objective 3 (pages 574–580).
    • Reading homework due on October 27 Monday (submit this in class or on Canvas): Which of these statements are always true and which are always false?
      1. x ≤ 4 and x > 5;
      2. x ≥ 2 or x < 3;
      3. 7 ≤ x < 6.
    • Problem set from the textbook due on October 29 Wednesday (submit this through MyLab): 8.6.43, 8.6.45, 8.6.47, 8.6.49, 8.6.51, 8.6.53, 8.6.55, 8.6.57, 8.6.59, 8.6.67, 8.6.69, 8.6.71, 8.6.73, 8.6.81, 8.6.83, 8.6.85, 8.6.87, 8.6.89, 8.6.91, 8.6.93.
25. Absolute-value inequalities:
    • Objectives:
      • Evaluate absolute values;
      • Test absolute-value statements;
      • Convert absolute-value inequalities into compound inequalities or compound statements;
      • Solve simple absolute-value inequalities.
    • Reading from (mostly) the textbook:
      • Section 8.7 introduction (page 584);
      • Section 8.7 Objectives 2&3 (pages 588–591);
      • My notes on absolute-value problems.
    • Reading homework due on October 29 Wednesday (submit this in class or on Canvas): Fill in the blanks with inequalities (possibly compound) that don't involve absolute values:
      1. |‍u| < a is equivalent to _____.
      2. |‍u| ≤ a is equivalent to _____.
      3. |‍u| > a is equivalent to _____ or _____.
      4. |‍u| ≥ a is equivalent to _____ or _____.
    • Problem set from the textbook due on October 31 Friday (submit this through MyLab): 8.7.69, 8.7.71, 8.7.73, 8.7.75, 8.7.77, 8.7.85, 8.7.87, 8.7.89, 8.7.91.
26. Absolute-value equations:
    • Objectives:
      • Convert absolute-value equations into compound statements;
      • Solve simple absolute-value equations;
      • Solve equations between absolute values.
    • Reading from the textbook: Section 8.7 Objective 1 (pages 584–587).
    • Reading homework due on October 31 Friday (submit this in class or on Canvas): Fill in the blanks with equations that don't involve absolute values:
      1. If a ≥ 0, then |‍u| = a is equivalent to _____ or _____.
      2. |‍u| = |‍v| is equivalent to _____ or _____.
    • Problem set from the textbook due on November 5 Wednesday (submit this through MyLab): 8.7.43, 8.7.47, 8.7.49, 8.7.51, 8.7.53, 8.7.55, 8.7.57, 8.7.59, 8.7.61, 8.7.63, 8.7.65, 8.7.103, 8.7.105, 8.7.107, 8.7.109.
27. Word problems with inequalities:
    • Objectives:
      • Set up compound inequalities to model situations where a quantity is bounded;
      • Set up absolute-value inequalities to model situations where a quantity's variation is bounded.
    • Reading from the textbook:
      • Section 8.6 Objective 4 (pages 580&581);
      • Section 8.7 Objective 4 (pages 591&592).
    • Reading homework due on November 5 Wednesday (submit this in class or on Canvas):
      1. Suppose that a and b are real numbers, with a ≤ b. If x must lie between a and b, inclusive, then what compound inequality expresses this fact?
      2. Suppose that c and e are real numbers, with e > 0. If x is meant to take the value c, with a tolerance of e, then what absolute-value inequality expresses this fact?
    • Problem set from the textbook due on November 7 Friday (submit this through MyLab): 8.6.101, 8.6.103, 8.6.105, 8.6.107, 8.6.109, 8.7.121, 8.7.123, 8.7.125, 8.7.127.

Relations and functions

28. Graphs:
    • Objectives:
      • Review the coordinate plane;
      • Graph equations using a table of values;
      • Find intercepts of the graph of an equation.
    • Reading from the textbook: Section 8.1 (pages 521–528).
    • Reading homework due on November 7 Friday (submit this in class or on Canvas):
      1. 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. A point on a graph that is also on a coordinate axis is a(n) _____ of that graph.
    • Problem set from the textbook due on November 12 Wednesday (submit this through MyLab): 8.1.17, 8.1.19, 8.1.21, 8.1.23, 8.1.25, 8.1.33, 8.1.39, 8.1.45, 8.1.49, 8.1.53, 8.1.55, 8.1.57.
29. Relations:
    • Objectives:
      • Graph a relation;
      • Find the domain of a relation;
      • Find the range of a relation.
    • Reading from the textbook: Section 8.2 (pages 531–535).
    • Reading homework due on November 12 Wednesday (submit this in class or on Canvas):
      1. The ordered pairs (a, b) and (c, d) are equal if and only if ___ = ___ and ___ = ___.
      2. If (3, 5) is on the graph of a relation, then 3 belongs to the _____ of the relation, and 5 belongs to its _____.
    • Problem set from the textbook due on November 14 Friday (submit this through MyLab): 8.2.27, 8.2.29, 8.2.31, 8.2.33, 8.2.39, 8.2.45, 8.2.49, 8.2.53.
30. Functions:
    • Objectives:
      • Evaluate a function;
      • Solve an equation to express one variable as a function of another;
      • Find the domain of a function from a formula.
    • Reading from the textbook: Section 8.3 (pages 538–546).
    • Reading homework due on November 14 Friday (submit this in class or on Canvas):
      1. Fill in the blank with a number: A function can be interpreted as a relation in which each element of the domain is related to ____ element(s) of the range.
      2. Fill in the blanks with variables: Given an equation in the variables x and y and assuming that it can be solved for ___, the equation represents y as a function of x if and only if there is at most one solution for each value of ____.
    • Problem set from the textbook due on November 17 Monday (submit this through MyLab): 8.3.35, 8.3.37, 8.3.39, 8.3.41, 8.3.43, 8.3.45, 8.3.47, 8.3.49, 8.3.51, 8.3.53, 8.3.55, 8.3.57, 8.3.59, 8.3.73, 8.3.75, 8.3.77, 8.3.79.
31. Graphs of functions:
    • Objectives:
      • Identify a graph as the graph of a function;
      • Graph a function using a table of values;
      • Find the domain and range of a function from a graph.
    • Reading from the textbook: Section 8.4 (pages 549–555).
    • Reading homework due on November 17 Monday (submit this in class or on Canvas): Fill in the blanks with mathematical expressions:
      1. 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.
      2. If (3, 5) is a point on the graph of a function f, then f(___) = ___.
      3. If g(2) = 4 for a function g, then _____ is a point on the graph of g.
    • Problem set from the textbook due on November 19 Wednesday (submit this through MyLab): 8.4.17, 8.4.19, 8.4.22, 8.4.31, 8.4.33, 8.4.37, 8.4.39, 8.4.51, 10.2.77.
32. Quadratic functions:
    • Objectives:
      • Find the vertex of the graph of a quadratic function;
      • Find the intercepts of the graph of a quadratic function;
      • Graph a quadratic function.
    • Reading from (mostly) the textbook:
      • Section 10.4 (pages 724–733);
      • Section 10.5 (pages 736–746);
      • My notes on quadratic functions.
    • Reading homework due on November 19 Wednesday (submit this in class or on Canvas): Suppose that f(x) = ax² + bx + c for all x.
      1. Fill in the blank with the name of a geometric shape: The graph of a f is a _____.
      2. Fill in the blanks with algebraic formulas: The vertex of this graph has the coordinates (___, ___).
    • Problem set from the textbook due on November 21 Friday (submit this through MyLab): 10.4.17, 10.4.19, 10.4.21, 10.4.23, 10.5.15, 10.5.17, 10.5.23, 10.5.25, 10.5.27, 10.5.29, 10.5.63, 10.5.65.

Quizzes

1. Roots and radicals:
   • Date: September 8 Monday.
   • Corresponding problems sets: 1–5.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
2. More radicals:
   • Date: September 22 Monday.
   • Corresponding problems sets: 6–10.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
3. Quadratic equations:
   • Date: October 6 Monday.
   • Corresponding problems sets: 11–15.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
4. Dividing polynomials:
   • Date: October 20 Monday.
   • Corresponding problems sets: 16–19.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
5. More rational expressions:
   • Date: November 3 Monday.
   • Corresponding problems sets: 20–23.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
6. Inequalities and absolute values:
   • Date: November 10 Monday.
   • Corresponding problems sets: 24–27.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.
7. Relations and functions:
   • Date: November 24 Monday.
   • Corresponding problems sets: 28–32.
   • Help allowed: Your notes, calculator.
   • NOT allowed: Textbook, my notes, other people, websites, etc.

Final exam

For the exam, you may use one sheet of notes that you wrote yourself, but 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).

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