4-5 Writing a Function Rule

Quick Review

To write a function rule describing a real-world situation, it is often helpful to start with a verbal model of the situation.

Example

At a bicycle motocross (BMX) track, you pay $40 for a racing license plus $15 per race. What is a function rule that represents your total cost?

total cost = license  fee  +  fee per race · number of races totalcost . equals , license . fee , plus . feeperrace . middle dot . numberofraces

C = 40 + 15 · r c equals 40 plus 15 middle dot r

A function rule is C = 40 + 15 · r . c equals 40 plus 15 middle dot r .

Exercises

Write a function rule to represent each situation.

18. Landscaping The volume V remaining in a 243 -ft 3 243 , minusft cubed  pile of gravel decreases by 0.2  ft 3 0.2 , ft cubed  with each shovelful s of gravel spread in a walkway.
19. Design Your total cost C for hiring a garden designer is $200 for an initial consultation plus $45 for each hour h the designer spends drawing plans.

4-6 Formalizing Relations and Functions

Quick Review

A relation pairs numbers in the domain with numbers in the range. A relation may or may not be a function.

Example

Is the relation {(0, 1), (3, 3), (4, 4), (0, 0)} a function?

The x-values of the ordered pairs form the domain, and the y-values form the range. The domain value 0 is paired with two range values, 1 and 0. So the relation is not a function.

Exercises

Tell whether each relation is a function.

20. {(−1, 7), (9, 4), (3, − 2 negative 2 ), (5, 3), (9, 1)}
21. {(2, 5), (3, 5), (4, − 4 negative 4 ), (5, − 4 negative 4 ), (6, 8)}

Evaluate each function for x = 2 and x = 7.

22. f ( x ) = 2 x − 8 f open x close equals 2 x minus 8
23. h ( x ) = − 4 x + 61 h open x close equals negative 4 x plus 61
24. The domain of t ( x ) = − 3.8 x − 4.2 t open x close equals negative 3.8 x minus 4.2  is { − 3 , − 1.4 , 0 , 8 } . left brace negative 3 comma negative 1.4 comma 0 comma 8 right brace .  What is the range?

4-7 Sequences and Functions

Quick Review

A sequence is an ordered list of numbers, called terms, that often forms a pattern. In an arithmetic sequence, there is a common difference between consecutive terms.

Example

Tell whether the sequence is arithmetic.

Exercises

Describe a pattern in each sequence. Then find the next two terms of the difference.

25. 1, 5, 25, 125, …
26. − 2 , − 5 , − 8 , − 11 , … negative 2 comma negative 5 comma negative 8 comma negative 11 comma dot dot dot
27. 4, 6.5, 9, 11.5, …
28. 2 , − 4 , 8 , − 16 , … 2 comma negative 4 comma 8 comma negative 16 comma dot dot dot

Tell whether the sequence is arithmetic. If it is, identify the common difference.

29. 2.9, 4.1, 5.3, 6.5, …
30. − 15 , − 5 , 5 , 15 , … negative 15 comma negative 5 comma 5 comma 15 comma dot dot dot
31. − 7 , − 13 , − 20 , − 26 , … negative 7 comma negative 13 comma negative 20 comma negative 26 comma dot dot dot
32. 3, 6, 12, 24, …

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