1. Homework, Page 253
Solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. 1.

2. Homework, Page 253
Solve the equation algebraically. Support your answer numerically and identify any extraneous solutions. 5.

3. Homework, Page 253
Solve the equation algebraically and graphically. Check for extraneous solutions. 9.

4. Homework, Page 253
Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically.
13.

5. Homework, Page 253
Solve the equation algebraically. Check for extraneous solutions. Support your answer graphically.
17.

6. Homework, Page 253 21. Both are extraneous.
Two possible solutions to the equation f (x) = 0 are listed. Use
the given graph of y = f (x) to decide which, if any are extraneous.
21.
Both are extraneous.

7. Homework, Page 253
Solve the equation.
25.

8. Homework, Page 253
Solve the equation.
29.

9. Homework, Page 253
33. Mid Town Sports Apparel has found that it needs to sell golf hats at $2.75 each to be competitive. It costs $2.12 to produce each hat, and weekly overhead is $3,000.
a. Let x be the number of hats produced each week. Express the average cost (including overhead) of producing one hat as a function of x.
b. Solve algebraically to find the number of golf hats that must be sold each week to make a profit. Support your answer graphically.
c. How many golf hats must be sold to make a profit of $1,000 in one week. Explain your answer.

10. Homework, Page 253
33. a. Let x be the number of hats produced each week. Express the average cost (including overhead) of producing one hat as a function of x.
b. Solve algebraically to find the number of golf hats that must be sold each week to make a profit.

11. Homework, Page 253
33. c. How many golf hats must be sold to make a profit of $1,000 in one week. Explain your answer.
To break even, 4,762 hats must be sold. After breaking even, a profit of $0.63 is made on each hat sold, so selling a total of 6,350 hats will yield a $1,000 profit.

12. Homework, Page 253
37. Drake Cannery will pack peaches in 0.5-L cylindrical cans. Let x be the radius of the can in cm.
a. Express the surface area of the can S as a function of x.

13. Homework, Page 253
37. b. Find the radius and height of the can if the surface area is 900 cm2.

14. Homework, Page 253
41. Drains A and B are used to empty a swimming pool. Drain A alone can empty the pool in 4.75 h. Let t be the time it takes for drain B alone to empty the pool.
a. Express as a function of t the part D of the drainage that can be done in 1 h with both drains open at the same time.
b. Find graphically the time it takes for drain B alone to empty the pool if both drains, when open at the same time, can empty the pool in 2.6 h. Confirm algebraically.

15. Homework, Page 253
41. a. Express as a function of t the part D of the drainage that can be done in 1 h with both drains open at the same time.

16. Homework, Page 253
41. b. Find graphically the time it takes for drain B alone to empty the pool if both drains, when open at the same time, can empty the pool in 2.6 h. Confirm algebraically.

17. Homework, Page 253
45. True – False An extraneous solution of a rational equation is also a solution of the equation. Justify your answer.
False. An extraneous solution is a solution of an equation obtained by multiplying or dividing each term of a rational equation by an expression containing a variable. The extraneous solution is a solution of the resulting equation, but not of the original equation.

18. Homework, Page 253
49. Which of the following are solutions of the equation a. b. c. d.
e. There are no solutions.

19. Homework, Page 253
Solve for x.
53.

20. Solving Inequalities in One Variable
2.8
Solving Inequalities in One Variable

21. What you’ll learn about
Polynomial Inequalities
Rational Inequalities
Other Inequalities
Applications
… and why
Designing containers as well as other types of
applications often require that an inequality be solved.

22. Polynomial Inequalities

23. Example Finding where a Polynomial is Zero, Positive, or Negative

24. Example Solving a Polynomial Inequality Analytically

25. Example Solving a Polynomial Inequality Graphically

26. Example Creating a Sign Chart for a Rational Function

27. Example Solving an Inequality Involving a Rational Function

28. Example Solving an Inequality Involving a Radical

29. Example Solving an Inequality Involving an Absolute Value

30. Homework
Review Section 2.8
Page 264, Exercises: 1 – 69 (EOO)
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