Free Printable Rational Function Test

1.

Simplify: $\frac{2x^2-11x+12}{x^2+2x-24}$

a)

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

b)

$\frac{\left(x-12\right)\left(2x+1\right)}{\left(x+6\right)\left(x-4\right)}$

c)

$\frac{\left(x-3\right)\left(x-8\right)}{\left(x+6\right)\left(x-4\right)}$

d)

$\frac{2x-3}{x+6}$

2.

What are the restrictions on x? $\frac{x^3+x^2-12x}{x^2-9}\cdot\frac{x-9}{x^2+4x}$

a)

$x\ne-9,\ -4\ ,\ 0$

b)

$x\ne-4,\ -3,\ 0,\ 3$

c)

$x\ne-4,\ 9$

d)

$x\ne-4,\ -3,\ 3$

3.

Divide: $\frac{x^2+3x-10}{x^2+6x+5}\div\frac{x^2-8x+12}{x^2-7x-8}$

a)

$\frac{x-8}{x-6}$

b)

$\frac{\left(x-2\right)^2\left(x-6\right)}{\left(x+1\right)^2\left(x-8\right)}$

c)

$\frac{\left(x+1\right)\left(x+5\right)\left(x-8\right)}{\left(x+2\right)\left(x+3\right)\left(x-6\right)}$

d)

$\frac{x-8}{x+6}$

4.

Add: $\frac{7}{x+6}+\frac{3}{x-1}$

a)

$\frac{10x+25}{\left(x+6\right)\left(x-1\right)}$

b)

$\frac{10x+11}{x+6}$

c)

$\frac{5}{x+6}$

d)

$\frac{10x+11}{\left(x+6\right)\left(x-1\right)}$

5.

Subtract: $\frac{8}{x^2-x-2}-\frac{3}{x^2-4}$

a)

$\frac{5x+1}{\left(x-2\right)\left(x+2\right)\left(x+1\right)}$

b)

$\frac{11x+19}{\left(x-2\right)\left(x+2\right)\left(x+1\right)}$

c)

$\frac{5x+13}{\left(x-2\right)\left(x+2\right)\left(x+1\right)}$

d)

$\frac{5x+19}{\left(x-2\right)\left(x+2\right)\left(x+1\right)}$

6.

Solve: $\frac{4}{x^2-4}-\frac{2}{x}=\frac{x+2}{x^2-4}$

a)

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

b)

$x=2$

c)

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

d)

No Solution

7.

What is the LCD: $\frac{x^3+x^2-12x}{x^2-9}\cdot\frac{x-9}{x^2+4x}$

a)

$\left(x+2\right)\left(x-2\right)\left(x+3\right)\left(x-3\right)$

b)

$\left(x+6\right)\left(x-3\right)\left(x^2-4x\right)$

c)

$x\left(x+9\right)\left(x-4\right)$

d)

$x\left(x+3\right)\left(x-3\right)\left(x+4\right)$

8.

You can find the x-intercept by setting the _______________ equal to 0 and solving for x.

a)

Numerator

b)

Denominator

c)

Canceled Factor

d)

None of the Above

9.

You can find the Vertical Asymptote by setting the ____________ equal to 0 and solve for x.

a)

Numerator

b)

Denominator

c)

Canceled Factor

d)

None of the Above

10.

You can find the holes in the graph by setting the ____________ equal to 0 and solving for x.

a)

Numerator

b)

Denominator

c)

Canceled Factors

d)

None of the Above

11.

If the degree of the numerator is greater that the degree of the denominator the Horizontal Asymptote is

a)

$y=0$

b)

$y=1$

c)

There is no H.A.

d)

$y=\frac{L.C.\ of\ num.}{L.C.\ of\ den.}$

12.

If the degree of the denominator is greater than the degree of the numerator than the Horizontal Asymptote is

a)

$y=0$

b)

$y=1$

c)

There is no H.A.

d)

$y=\frac{L.C.\ of\ Num.}{L.C.\ of\ Den.}$

13.

$\frac{5x-10}{x^2-4}$ What are the vertical and Horizontal Asymptote of

a)

$x=-2,\ 2\ ;\ y=5$

b)

$x=-2\ ;\ y=0$

c)

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

d)

$x=-2\ ;\ y=5$

14.

$\frac{5x-10}{x^2-4}$ What is the hole:

a)

There's no Hole

b)

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

c)

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

d)

$\left(2,\ \frac{5}{4}\right)$

15.

What is the x- and y- intercept of $\frac{5x-10}{x^2-4}$

a)

$x-\ int\ \left(5,\ 0\right)\ ;\ y\ -int\ \left(0,\ \frac{5}{2}\ \right)$

b)

$x-int\ \left(-2,\ 0\right)\ ;\ y-int\ \left(0,\ \frac{5}{2}\right)$

c)

$x-int\ :\ none\ ;\ y-int\ \left(0,\ \frac{5}{2}\right)$

d)

$x-int:\ none\ ;\ y-int:\ none$

16.

The domain of a rational function excludes what?

a)

Vertical Asymptote and x value in the hole

b)

Vertical Asymptote and x- intercept

c)

Vertical Asymptote, Horizonal Asymptote, and x value of the hole

d)

Vertical Asymptote, x- intercept, and x value of the hole

17.

The range of a rational function excludes what?

a)

Vertical Asymptote, Horizontal Asymptote, y value in the hole

b)

Horizontal Asymptote, y- intercept, y- value in the hole

c)

Vertical Asymptote and Horizontal Asymptote

d)

Horizontal Asymptote and y value in the hole

18.

What are the vertical and horizontal asymptotes of: $\frac{x^2+4x-32}{x^2-5x+4}$

a)

$x=1\ and\ y=1$

b)

$x=1\ and\ y=-8$

c)

$x=1,\ 4\ and\ y=1$

d)

$x=1,\ 4\ and\ y=-8$

19.

What is the hole: $\frac{x^2+4x-32}{x^2-5x+4}$

a)

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

b)

$\left(-4,\ \frac{4}{5}\right)$

c)

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

d)

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

20.

What is the x- and y-intercept of $\frac{x^2+4x-32}{x^2-5x+4}$

a)

$x-int\ \left(-8,\ 0\right)\ and\ \left(4,\ 0\right)\ \ ;\ y-int\ \left(0,\ -8\right)$

b)

$x-int\left(-8,\ 0\right)\ ;\ y-int\ \left(0,\ -8\right)$

c)

$x-int\ \left(-8,\ 0\right)\ ;\ y-int\ \left(0,\ 8\right)$

d)

$x-int\ \left(-8,\ 0\right)\ ;\ \ y-int\ \left(0,\ 1\right)$

Rational Function Test

Total questions: 20

Worksheet time: 29mins

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