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2. Lesson 7-1 Polynomial Functions
Lesson 7-2 Graphing Polynomial Functions
Lesson 7-3 Solving Equations Using Quadratic Techniques
Lesson 7-4 The Remainder and Factor Theorems
Lesson 7-5 Roots and Zeros
Lesson 7-6 Rational Zero Theorem
Lesson 7-7 Operations on Functions
Lesson 7-8 Inverse Functions and Relations
Lesson 7-9 Square Root Functions and Inequalities
Contents

3. Example 1 Add and Subtract Functions
Example 2 Multiply and Divide Functions
Example 3 Evaluate Composition of Relations
Example 4 Simplify Composition of Functions
Example 5 Use Composition of Functions
Lesson 7 Contents

4. Given , find
Addition of functions
and
Simplify.
Answer:
Example 7-1a

5. Subtraction of functions
Given , find
Subtraction of functions
and
Simplify.
Answer:
Example 7-1b

6. Given find each function.b.
Answer:
Answer:
Example 7-1c

7. Distributive Property
Given find
Product of functions
and
Distributive Property
Distributive Property
Simplify.
Answer:
Example 7-2a

8. Given find
Division of functions
Answer:
and
Example 7-2b

9. Since 4 makes the denominator 0, it is excluded from the domain of
Example 7-2c

10. Given find each function.b.
Answer:
Answer:
Example 7-2d

11. If f (x) = {(2, 6), (9, 4), (7, 7), (0, –1)} and g (x) = {(7, 0), (–1, 7), (4, 9), (8, 2)}, find and
To find , evaluate g (x) first. Then use the range of g as the domain of f and evaluate f (x).
Answer:
Example 7-3a

12. Answer: Since 6 is not in the domain of g, is undefined for x = 2.
To find evaluate f (x) first. Then use the range of f as the domain of g and evaluate g (x).
is undefined.
Answer: Since 6 is not in the domain of g, is undefined for x = 2.
Example 7-3b

13. If f (x) = {(1, 2), (0, –3), (6, 5), (2, 1)} and g (x) = {(2, 0), (–3, 6), (1, 0), (6, 7)}, find and
Answer:
Example 7-3c

14. Composition of functions
Find and and
Composition of functions
Replace g (x) with 2x – 1.
Substitute 2x – 1 for x in f (x).
Example 7-4a

15. Composition of functions
Evaluate (2x – 1)2.
Simplify.
Composition of functions
Replace f (x) with
Example 7-4b

16. Substitute for x in g (x).
Simplify.
Answer: So, and
Example 7-4c

17. Evaluate and x = –2. Function from part a Replace x with –2. Simplify.
Example 7-4d

18. Function from part a Replace x with –2. Simplify. Answer: So, and
Example 7-4e

19. a. Find and and b. Evaluate and x = 1. Answer: and Answer: and
Example 7-4f

20. Taxes Tracie Long has $100 deducted from every paycheck for retirement
Taxes Tracie Long has $100 deducted from every paycheck for retirement. She can have this deduction taken before state taxes are applied, which reduces her taxable income. Her state income tax is 4%. If Tracie earns $1500 every pay period, find the difference in her net income if she has the retirement deduction taken before or after state taxes.
Explore Let x = her income per paycheck, r (x) = her income after the deduction for retirement, t (x) = her income after tax.
Example 7-5a

21. $100 is deducted for retirement.
Plan Write equations for r (x) and t (x).
$100 is deducted for retirement.
The tax rate is 4%.
Solve If Tracie has her retirement deducted before taxes, then her net income is represented by
Replace x with in
Example 7-5b

22. Replace x with in
If Tracie has her retirement deducted after taxes, then her net income is represented by
Replace x with 1500 in
Example 7-5c

23. Replace x with in
Answer: and The difference is 1344 – 1340 or 4. So, her net income is $4 more if the retirement deduction is taken before taxes.
Examine The answer makes sense. Since the taxes are being applied to a smaller amount, less taxes will be deducted from her paycheck.
Example 7-5d

24. Taxes Brandi Smith has $200 deducted from every paycheck for retirement. She can have this deduction taken before state taxes are applied, which reduces her taxable income. Her state income tax is 10%. If Brandi earns $2200 every pay period, find the difference in her net income if she has the retirement deduction taken before or after state taxes.
Answer: Her net income is $20 more if she has the retirement deduction taken before her state taxes.
Example 7-5e

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26. Transparency 1a

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28. Transparency 2a

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30. Transparency 8a

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32. Transparency 9a