1. Chapter 7.7 Operations on Functions Standard & Honors
Algebra II Mr. Gilbert
Chapter 7.7
Operations on Functions
Standard & Honors
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2. Agenda Warm up Homework Review Lesson Test Homework 11.7 Pascal return
Bonus Opportunity
Homework
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3. Click the mouse button or press the Space Bar to display the answers.
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Click the mouse button or press the Space Bar to display the answers.
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5. Homework Review
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6. Communicate Effectively
Range
Domain
Function
Order of Operations
Composite function
Building a cell phone business: How much to spend on manufacturing, repair, getting customers?
The cost of the manufacturing? (build it cheaply or robustly)
The cost of warrantee? (repair or replace)
The cost of a customer? (how to get and keep customers)
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7. 7-7 Operations on Functions
Example 1 Add and Subtract Functions (3)
Example 2 Multiply and Divide Functions (4)
Example 3 Evaluate Composition of Relations (3)
Example 4 Simplify Composition of Functions (6)
Example 5 Use Composition of Functions (6)
Question:
How should a company spend to manufacture a
a cell phone?
The cost of the manufacturing? (build it cheaply or robustly)
The cost of warrantee? (repair or replace)
The cost of a customer? (how to get and keep customers)
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Lesson 7 Contents

8. Given , find Addition of functions and Simplify. Answer: 5/14/2019
Example 7-1a

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

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

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

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

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

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

15. 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:
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Example 7-3a

16. 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.
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Example 7-3b

17. 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:
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Example 7-3c

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

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

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

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

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

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

24. 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.
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Example 7-5a

25. $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
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Example 7-5b

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

27. 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.
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Example 7-5d

28. 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.
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Example 7-5e

29. Homework - Honors See Syllabus 7.7
pp : even, odd, 47-56
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30. Homework See Syllabus 7.7 pp. 387- 388 17-26, 29-30, 35-45 odd, 47-55
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