Practice and Problem-Solving Exercises

A Practice

See Problem 1.

Graph each function. Identify the x- and y-intercepts and the asymptotes of the graph. Also, state the domain and the range of the function.

8. y = 2 x y equals , 2 over x
9. y = 15 x y equals , 15 over x
10. y = − 3 x y equals , negative 3 over x
11. y = − 10 x y equals negative , 10 over x
12. y = 10 x y equals , 10 over x

See Problem 2.

Graphing Calculator Graph the equations y = 1 x y equals , 1 over x  and y = a x y equals , eh over x  using the given value of a. Then identify the effect of a on the graph.

13. a = 2 eh equals 2
14. a = − 4 eh equals negative 4
15. a = 0. 5 eh equals 0. 5
16. a = 12 eh equals 12
17. a = 0. 75 eh equals 0. 75

See Problem 3.

Sketch the asymptotes and the graph of each function. Identify the domain and range.

18. y = 1 x − 3 y equals , 1 over x , minus 3
19. y = − 2 x − 3 y equals , negative 2 over x , minus 3
20. y = 1 x − 2 + 5 y equals . fraction 1 , over x minus 2 end fraction . plus 5
21. y = 1 x − 3 + 4 y equals . fraction 1 , over x minus 3 end fraction . plus 4
22. y = 2 x + 6 − 1 y equals . fraction 2 , over x plus 6 end fraction . minus 1
23. y = 10 x + 1 − 8 y equals . fraction 10 , over x plus 1 end fraction . minus 8
24. y = 1 x − 2 y equals , 1 over x , minus 2
25. y = − 8 x + 5 − 6 y equals . fraction negative 8 , over x plus 5 end fraction . minus 6

See Problem 4.

Write an equation for the translation of y = 2 x y equals , 2 over x  that has the given asymptotes.

26. x = 0 x equals 0  and y = 4 y equals 4
27. x = − 2 x equals negative 2  and y = 3 y equals 3
28. x = 4 x equals 4  and y = − 8 y equals negative 8

    See Problem 5.

29. Construction The weight P in pounds that a beam can safely carry is inversely proportional to the distance D in feet between the supports of the beam. For a certain type of wooden beam, P = 9200 D . p equals , 9200 over d , .  What distance between supports is needed to carry 1200 lb?

B Apply

30. Think About a Plan A high school decided to spend $750 on student academic achievement awards. At least 5 awards will be given, they should be equal in value, and each award should not be less than $50. Write and sketch a function that models the relationship between the number a of awards and the cost c of each award. What are the domain and range of the function?
    • Which equation describes the relationship between a and c?
    • What information can you use to determine the domain and range?

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