Rational Functions Practice Test

MHF4U1

RATIONAL FUNCTIONS PRACTICE TEST

Multiple Choice  Identify the letter of of the choice that best completes completes the statement statement or answers the question. question.

 ____

1. What is the x the x-intercept -intercept of the function

?

a.  x =  x = 1 and x and x = 4  b.  x = 1  ____

 ____

 ____

c.  x =  x =  – 4 d.  x =  x = 4

2. What is the domain of the the function

?

a.

c.

 b.

d.

3. What is the oblique oblique asymptote for

?

a.

c.

 b.

d.

4. Which of the following following functions does not not have a vertical asymptote? asymptote? a. c.

 b.

 ____

d.

5. Which of the following following functions does not not have a horizontal asymptote? asymptote? a. c.

 b.

 ____

6. What are the zeros of a.  b.

 ____

d.

? c. d.

7. Which of the following following statements is false false for the function

where both  g  and  and h are

 polynomial functions? functions? a. It is possible to have both a vertical asymptote asymptote and and a horizontal horizontal asymptote. asymptote.  b. It is possible to have both both an oblique asymptote asymptote and a horizontal asymptote. asymptote. c. It is possible to have both a vertical asymptote asymptote and and an oblique oblique asymptote. asymptote. d. It is impossible impossible to have an oblique oblique asymptote, asymptote, a horizontal horizontal asymptote, asymptote, and a vertical asymptote.

 ____

8. What is the horizontal horizontal asymptote of

?

a.  b.

 ____

c. d.

9. What are the vertical asymptotes asymptotes of a.  b.

?

and and

c. d.

and

 ____ 10. Which of the following following functions has an oblique oblique asymptote? a. c.

 b.

d.

 ____ 11. Which of the following following functions has a vertical vertical asymptote at a. c.

 b.

and a horizontal asymptote asymptote of

d.

 ____ 12. Which equation represents represents the following graph? a.

c.

 b.

d.

 ____ 13. What is the domain of the the following function? function?

a.

c.

 b.

d.

?

 ____ 14. Describe the characteristics characteristics of the function

?

a. the vertical asymptote is x is  x = -2  b. the horizontal asymptote asymptote is y is  y = 0

c. the oblique asymptote is y is  y =  = x  x  - 2 d. there is a point discontinuity discontinuity

 ____ 15. For which function below below does a.

when c.

 b.

?

d.

 ____ 16. Which function below below has no horizontal asymptote? a. c.

 b.

d.

17.

Solve

4 x  x

2



5x 3x  1 1

18. a) Solve using critical points  x

3

 4

 b) Sketch the two functions and shade the area that satisfies the inequality.

19. Sketch

f ( x ) 

5 x   2 , showing all asymptotes and intercepts on your graph.  x   3

20. a) For the function

 −3 2−3  +2 − 3 +2(−5) − 5)

determine the asymptotes, domain, intercepts and

 behavior as f(x) as f(x) approaches  approaches the vertical asymptote  b) Use the information to sketch the graph of the function.

Text book questions: Pg 309 #9 Pg 262 #1 –  make  make sure you can explain your answer.

Answers: 1) A 11) D

2) B 3) B 4) C 5) A 6) C 7) B 12) C 13) D 14) B 15) B 16) C

17) x = 0 or 6/7 18)  < −3,  ≥ −2.75

4

g(x ) = 4

2

5

f(x ) =

5

1

2

 x  +  + 3

4

19)

1

16

14

12

10

h( ) =

5∙

8

2  + 3

6

4

2

10

5

5 2

20) b. 4

q(x ) =

 x  3

3

(2∙ x   x  3)∙( x  +  + 2)∙( x  5) 2

1

10

5

5 1

2

3

4

8) D

9) A

10) B