Free Printable Graphing Rational Functions

1.

Select ALL the information that applies to the given rational function.
$f\left(x\right)=\frac{x-3}{-2x^2+8x-6}$

a)

Vertical Asymptote. at x = 1

b)

No Holes

c)

Horizontal Asymptote. at y = 0

d)

y-intercept at (0, 1/2)

2.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{2x^2-2}{x^2-4x+3}$

a)

Vertical Asymptote. at x = -3 and x = 1

b)

Hole at (1, 0)

c)

Horizontal Asymptote at y = 2

d)

x-intercepts at (3,0) and (1, 0)

3.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x^2-x}{-4x+16}$

a)

Vertical Asymptote. at x = -1

b)

No Holes

c)

Horizontal Asymptote. at y = -1/4

d)

x-intercepts at (0,0) and (-1,0)

4.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x+3}{-3x+6}$

a)

Vertical Asymptote at x = 2

b)

No Holes

c)

Horizontal Asymptote at y = -1/3

d)

y-intercepts at (0, 1/2)

5.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{1}{-3x^2-9}$

a)

No Vertical Asymptote

b)

No Holes

c)

Slant (Oblique) Asymptote at $y=x-3$

d)

No x-intercept

6.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x^3+2x^2-3x+5}{x^2-3x+4}$

a)

Vertical Asymptote at x = 3 and x = -1

b)

No Holes

c)

Slant (Oblique) Asymptote at y = x + 5

d)

y-intercept at (0,0)

7.

Graph the function.

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

a)

b)

c)

d)

8.

Graph the function.

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

a)

b)

c)

d)

9.

$f\left(x\right)=\frac{2x^2+x+1}{x+1}$ Graph the function.

a)

b)

c)

d)

10.

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)

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

11.

Which of the following represents the graph below?

a)

b)

c)

d)

Graphing Rational Functions

Total questions: 11

Worksheet time: 3hrs 45mins

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