NAME:______

DATE:______

Rational Functions Unit Test

Multiple Choice

____ 1. Which of the following has a horizontal asymptote at ?

a. / / c. /
b. / / d. / all of the above

____ 2. What is the value of k in the function if its graph passes through the point (5, –0.35) ?

a. / 10 / c. /
b. / / d. / No such k exists

____ 3. Which function has vertical asymptotes and ?

a. / / c. /
b. / / d. / all of the above

____ 4. What is the equation for the horizontal asymptote of the graph of the function shown?

a. / / c. /
b. / / d. /

____ 5. What are the x-intercepts of the graph of ?

a. / –4, 5 / c. / 4, –5
b. / –7, 3 / d. / 7, –3

____ 6. Which of the following has no solution?

a. / / c. /
b. / / d. / all of the above

____ 7. Use the graph of to solve the equation .

a. / / c. /
b. / / d. / no solution

____ 8. Use the graph of to solve the inequality .

a. / / c. /
b. / / d. / no solution

____ 9. Which of the following functions has a slant asymptote when graphed?

a. / / c. /
b. / / d. /

____ 10. Which of the following functions has a hole at x = 5?

a. / / c. /
b. / / d. / B and C

Problem Solving

1.  Graph the following:

a.  b.

2.  Determine the asymptotes of .

3.  Write the equation of rational function with vertical asymptotes of x = 1 and x = -1, horizontal asymptote of y = 3/2 and x-intercepts of 3 and -3.

4.  Solve

a.  b.

5.  Solve

a.  b.

6.  Explain how the graph of is the same and different from the graph of .

7.  Explain how you can use the expressions in the numerator and the denominator of a rational function to decide if the graph has an oblique (slant) asymptote and what that asymptote would be.

8.  A rectangular garden with an area of 250 square metres is to be located next to a building and fenced on three sides, with the building acting as a fence on the fourth side.

a.  If the side of the garden parallel to the building has length x metres, express the amount of fencing needed as a function of x.

b.  For what values of x will less than 60 metres of fencing be needed?

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