Free Printable Unit 4 Rational Function Review

1.

What is the vertical asymptote?

f\left(x\right)=\frac{x+4}{x^2+x-12}

a)

x = -4

b)

x = -3

c)

y = 1

d)

x = 3

2.

What is the horizontal asymptote?

f\left(x\right)=\frac{x-7}{x}

a)

x = 0

b)

x = 7

c)

y = 1

d)

DNE

3.

What is the horizontal asymptote?

f\left(x\right)\ =\ \frac{2x^2-5x+1}{x^2-x}

a)

y = 2

b)

y = 1

c)

y = 0

d)

DNE

4.

State the vertical asymptotes:

f\left(x\right)=\frac{2}{x^2+3x-4}

a)

$x=1,\ \ x=-3$

b)

$x=1,\ \ x=-4$

c)

$x=2,\ \ x=3$

d)

$x=2,\ \ x=-\frac{3}{4}$

5.

The horizontal asymptote is y = 0 when:

a)

the exponents in the numerator and denominator are equal

b)

the exponents in the numerator are less than the denominator

c)

the exponents in the numerator are greater than the denominator

d)

the numerator equals zero

6.

The holes of a rational function occur when :

a)

my pencil pokes a hole in the paper I'm working on

b)

there is something left in the denominator

c)

the value of f(0)

d)

a factor in the denominator cancels with a factor in the numerator

7.

A rational function is ...?

a)

a line that continually approaches a given curve but does not meet it at any finite distance.

b)

The top of a rational expression

c)

The bottom of a rational expression

d)

Made up of a ratio (fraction) of two polynomials

8.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

slant

d)

none

9.

Find the vertical asymptote(s).

f\left(x\right)=\frac{4}{x-4}

a)

None

b)

x = 0

c)

x = 4

d)

x = -4 and x = 4

10.

Where is the hole of the given rational function?

f\left(x\right)=\frac{x^2-9x+20}{x^2-3x-10}

a)

$\left(5,\ \frac{1}{28}\right)$

b)

$\left(4,\ 0\right)$

c)

$\left(5,\ \frac{1}{7}\right)$

d)

$\left(-2,\ 0\right)$

11.

State the vertical asymptote for the following rational function:

f\left(x\right)=\frac{x^2-2x}{x+5}

a)

$x=-\frac{2}{5}$

b)

$x=\frac{5}{2}$

c)

$x=-5$

d)

$x=2$

12.

Find the vertical asymptote for the following rational function.

f\left(x\right)=\frac{x^2-2x-8}{3x-2}

a)

$y=\frac{2}{3}$

b)

$x=\frac{3}{2}$

c)

$x=\frac{2}{3}$

d)

$x=\frac{1}{3}$

13.

What are the asymptotes?

a)

x = -1, y = -3

b)

x = 1, y = -3

c)

x = -1, y = 3

d)

x = 1, y = 3

14.

Find the x-intercept (zero) of the function

f\left(x\right)=\frac{x-7}{x}

a)

(0, 0)

b)

(0, -7)

c)

(7, 0)

d)

there is no x- intercept

15.

What are the asymptotes of this rational function.

a)

x = 1, x = 2, y = 1, y = 2

b)

x = 2, x = -2, y = 1

c)

x = 1, y = 1

d)

x =-1, y = 2, y = -2

16.

What coordinate has a hole?

f\left(x\right)=\frac{x+4}{x^2+x-12}

a)

$DNE$

b)

$\left(-4,\ -\frac{1}{7}\right)$

c)

$\left(4,\ 0\right)$

d)

$\left(-4,-1\right)$

17.

Where is there a hole?

f\left(x\right)=\frac{x+2}{x^2+x-12}

a)

$DNE$

b)

$\left(2,\ -\frac{2}{3}\right)$

c)

$\left(3,\frac{5}{7}\right)$

d)

$\left(4,\frac{3}{4}\right)$

18.

Find the x-intercept (zero) of the function

f\left(x\right)=\frac{2x^2+7x+3}{x-5}

a)

$\left(0,0\right)\ \ \ \left(-\frac{1}{2},0\right)\ \ \ \left(-3,0\right)$

b)

$\left(5,0\right)$

c)

$\left(-\frac{1}{2},0\right)\ \ \ \left(-3,0\right)$

d)

$\left(\frac{1}{2},0\right)\ \ \ \left(3,0\right)$

19.

Graph the function.

f\left(x\right)=\frac{-x+1}{x-4}

a)

b)

c)

d)

20.

Match the graph to the correct rational equation below.

a)

$f(x)=\frac{x^2}{x^2+x-12}$

b)

$f(x)=\frac{4x^2}{x^2-x-12}$

c)

$f(x)=\frac{2x^2-2}{2x^2}$

d)

$f(x)=\frac{x}{x^2+x-12}$

21.

What is the first step in graphing rational functions?

a)

Vertical Asymptotes

b)

X-intercepts

c)

Factor

d)

End behavior model

22.

How do you find holes in a rational function?

a)

Factors that cancel

b)

Set denominator = 0

c)

Set numerator = 0

d)

Substitute 0 for x

23.

How do you find vertical asymptotes in a rational function?

a)

Substitute 0 for x

b)

Set denominator = 0

c)

Set numerator = 0

d)

Factors that cancel

24.

How do you find x-intercepts in a rational function?

a)

Substitute 0 for x

b)

Set denominator = 0

c)

Set numerator = 0

d)

Factors that cancel

25.

How do you find y-intercepts in a rational function?

a)

Substitute 0 for x

b)

Set denominator = 0

c)

Set numerator = 0

d)

Factors that cancel

26.

Find the domain of the function.

f\left(x\right)=\frac{x^2}{x+8}

a)

$All\ real\ numbers;\ x\ne2$

b)

$All\ real\ numbers;\ x\ne-2$

c)

$All\ real\ numbers;\ x\ne-8$

d)

$All\ real\ numbers$

27.

Graph the function.

$f\left(x\right)=\frac{-2x^2+2x+24}{x^3-x^2-12x}$

a)

b)

c)

d)

28.

What is the horizontal asymptote?

f\left(x\right)=\frac{x^2-4}{x^2-5x+6}

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

29.

Write a rational function with the given characteristics:
vertical asymptote at x = –4 , horizontal asymptote at y = –3, x-intercept at (2, 0), hole at (-1, -1), y-intercept at (0. -1/2)

a)

$f\left(x\right)=\frac{\left(x-1\right)\left(x+1\right)}{\left(x-3\right)\left(x-2\right)}$

b)

$f\left(x\right)=\frac{\left(x-2\right)\left(x+1\right)}{\left(x-3\right)\left(x-2\right)}$

c)

$f\left(x\right)=\frac{\left(x-1\right)\left(x+1\right)}{\left(x+4\right)\left(x-1\right)}$

d)

$f\left(x\right)=\frac{\left(x-2\right)\left(x+1\right)}{\left(x+4\right)\left(x+1\right)}$

30.

Which rational function below does NOT have a hole?

a)

$y=\frac{\left(x+10\right)\left(x-5\right)}{\left(x-10\right)\left(x+5\right)}$

b)

$y=\frac{2x-1}{2x-1}$

c)

$y=\frac{\left(x+3\right)^4}{x+3}$

d)

$y=\frac{\left(x-5\right)\left(x+6\right)}{\left(x+6\right)\left(x+2\right)}$

Unit 4 Rational Function Review

Total questions: 30

Worksheet time: 1hrs 19mins

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