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, –5b. / –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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