Chapter 9: Rational Functions Review

CHAPTER 9: RATIONAL FUNCTIONS REVIEW

1. Suppose that x and y vary inversely, and x = 7 when y = 9. Write the function that models the inverse variation.

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.

2.

3. Suppose that y varies directly with x and inversely with z y = 3 when x = 3, and z = 7. Write the equation that models the relationship. Then find y when x = 10 and z = 2.

4. A drama club is planning a bus trip to New York City to see a Broadway play. The cost per person for the bus rental varies inversely as the number of people going on the trip. It will cost $50 per person if 28 people go on the trip. How much will it cost per person if 56 people go on the trip? Round your answer to the nearest cent, if necessary.

Find the vertical asymptote(s) of the function.

5. 6.

Simplify the rational expressions. State any restrictions on the variables.

7.

Multiply or divide. State any restrictions on the variables.

8.

9.

10.

Add or subtract. Simplify if possible.

11.

12.

13.

14.

15. Simplify the complex fractions. 4x+11x+2

Solve each equation. Check your solution(s).

16. 5x+2=8x+4

17. 53a+84a=4

18. aa2-25+2a-5=1a+5

19. A group of college students are volunteering for Help the Homeless during their spring break. They are putting the finishing touches on a house they built. Working alone, Xavier can paint a certain room in 2 hours. David can paint the same room in 4 hours. Write an equation that can be used to find how long it will take them working together to paint the room. How many hours will it take them to paint the room? If necessary, round your answer to the nearest hundredth.

20. The values (9, 2) and (x, 3) are from an inverse variation. Find the missing value and round to the nearest hundredth.

21. The time t required to drive a certain distance varies inversely with the speed r. If it takes 3 hours to drive the distance at 150 miles per hour, how long will it take to drive the same distance at 45 miles per hour?

22. An enclosed gas exerts a pressure P on the walls of a container. This pressure is directly proportional to the temperature T of the gas. If the pressure is 8 lb per square inch. when the temperature is 480ºF, find the constant of variation.

23. Find the constant of variation k for the inverse variation. Then write an equation for the inverse variation.

y = 5 when x = 3.

24. Suppose that x and y vary inversely, and x = 11 when y = 9. Write the function that models the inverse variation.

Graph the function.

25. f(x) =

26. f(x) = + 1

27. Describe the vertical asymptote(s) and hole(s) for the graph

y=x+3(x-5)x-5(x+2)

28. Describe how the graph of gx=2x-5-3 is a translation of gx=2x .

29. gx=2x-5-3 . Find the vertical asymptote and the horizontal symptote.

30. Solve the equation. Check your solution. 3y+15y=-4