Rational Functions Practice Test
Rational Functions Practice Test
Multiple Choice
Identify the letter of the choice that best completes the statement or answers the question.
a. c.
b. d.
b. d.
____ 4. Which of the following functions does not have a vertical asymptote?
a. c.
b. d.
____ 5. Which of the following functions does not have a horizontal asymptote?
a. c.
b. d.
a. c.
b. d.
____ 7. Which of the following statements is false for the function where both g and h are
polynomial functions?
a. It is possible to have both a vertical asymptote and a horizontal asymptote.
b. It is possible to have both an oblique asymptote and a horizontal asymptote.
c. It is possible to have both a vertical asymptote and an oblique asymptote.
d. It is impossible to have an oblique asymptote, a horizontal asymptote, and a vertical
asymptote.
____ 8. What is the horizontal asymptote of ?
a. c.
b. d.
a. and c. and
b. and d.
b. d.
____ 11. Which of the following functions has a vertical asymptote at and a horizontal asymptote of ?
a. c.
b. d.
a. c.
b. d.
a. c.
b. d.
____ 14. Describe the characteristics of the function ?
a. the vertical asymptote is x = -2 c. the oblique asymptote is y = x - 2
b. the horizontal asymptote is y = 0 d. there is a point discontinuity
b. d.
b. d.
4x 5x
17. Solve
x 2 3x 1
1
18. a) Solve using critical points 4
x3
b) Sketch the two functions and shade the area that satisfies the inequality.
5x 2
19. Sketch f ( x ) , showing all asymptotes and intercepts on your graph.
x 3
𝑥−3
20. a) For the function determine the asymptotes, domain, intercepts and
2𝑥−3 𝑥+2 (𝑥−5)
behavior as f(x) approaches the vertical asymptote
17) x = 0 or 6/7
4
g( x ) = 4
5 5
1
f(x) = 2
x+3
19) 18
16
14
12
10
8
5∙x 2
h( x ) =
x+3 6
10 5 5
20) b.
x 3 3
q( x ) =
(2∙x 3)∙(x + 2)∙(x 5)
2
10 5 5