Free Printable Rational Function

1.

Given the function $f\left(x\right)\ =\ \frac{1}{4\ -\ x^2}$ find the vertical and horizontal asymptotes

a)

$x\ =\ 2\ and\ x\ =\ -\ 2,\ y\ =\ 0\$

b)

$x\ =\ 0\ ,\ y\ =\ -2\ and\ y\ =\ 2$

2.

Given the function $f\left(x\right)\ =\ \frac{x}{x^2-1}$ identify the vertical and horizontal asymptotes.

a)

$y\ =\ -\ 1\ and\ y\ =\ 1\ ;\ x\ =\ 0\$

b)

$x\ =\ -\ 1\ and\ x\ =\ 1\ ;\ y\ =\ 0\$

3.

Given the function $f\left(x\right)\ =\ \frac{\left(x\ +\ 2\right)}{\left(x\ -\ 1\ \right)}$ , identify the vertical and horizontal asymptotes.

a)

$x\ =\ 1,\ y\ =\ 1$

b)

$x\ =\ -1,\ y\ =\ 1$

4.

Given the function $f\left(x\right)=\ \frac{x^2+x\ -\ 3}{x^2+x\ -\ 12\ }$ , identify the vertical and horizontal asymptotes

a)

$x\ =\ -\ 4\ and\ x\ =\ 3\ ;\ y\ =\ 1$

b)

$x\ =\ 4\ ,\ and\ x\ =\ -3\ ;\ y\ =\ 1$

c)

$y\ =\ -4\ and\ y\ =\ 3\ ;\ x\ =\ 1$

5.

Given the function $f\left(x\right)\ =\ \frac{1\ -\ x^2}{x^{2\ }-\ 9\ }$ identify the vertical and horizontal asymptotes

a)

$x\ =\ -\ 3\ and\ x\ =\ 3\ ;\ y\ =\ 1$

b)

$x\ =\ -\ 3\ and\ x\ =\ 3\ ;\ y\ =\ -\ 1$

c)

$x\ =\ -1\ ;\ y\ =\ -\ 3\ and\ y\ =\ 3$

6.

Find the y intercept of the function $f\left(x\right)\ =\ \frac{x^2+x\ -\ 3\ }{x^{2\ }+\ x\ -\ 12}$

a)

$\left(0,\ \frac{1}{4}\right)$

b)

$\left(0,0\right)$

c)

$\left(0,\frac{-1}{4}\right)$

d)

$\left(\frac{1}{4},\ 0\right)$

7.

What is the y - intercept of the function $f\left(x\right)=\ \frac{x+2}{x-1}$ ?

a)

$2$

b)

$1$

c)

$-2$

d)

$-1$

8.

What is the x - intercept of the function $f\left(x\right)\ =\ \frac{1\ -\ x^2}{x^2-\ 9\ }$ ?

a)

$x\ =\ 0$

b)

$x\ =\ -\ 1$

c)

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

d)

$x\ =\ 1$

9.

What is the correct graph of the function $f\left(x\right)\ =\ \frac{x\ +2}{x\ -\ 2}$ ?

a)

b)

10.

Describe the behavior of the graph of the function $f\left(x\right)\ =\ \frac{\left(x+2\right)}{\left(x\ -\ 1\right)}$ from left to right?

a)

$As\ x\rightarrow1^-\ \ ,\ y\ =\ -\infty$

b)

$As\ x\ \rightarrow\ 1^{-1},\ y\ =\ \infty$

c)

$As\ x\ \rightarrow\ 1^+,\ y\ \rightarrow\infty$

d)

$As\ x\ \rightarrow1^+,\ \ y\ \rightarrow-\infty$

Rational Function

Total questions: 10

Worksheet time: 50mins

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