Free Printable Rational and Reciprocal Functions

1.

Which of the following represents the graph below?

a)

b)

c)

d)

2.

Which of the following represent the graph?

a)

b)

c)

d)

3.

Describe the transformation of the function.

a)

shift left 3 units

b)

shift right 3 units

c)

shift up 3 units

d)

shift down 3 units

4.

Describe the transformations of the function.

a)

Shift up by 2 units

Reflected over the x-axis

b)

Shift down by 2 units

Reflected over the y-axis

c)

Shift up by 2 units

Reflected over the y-axis

d)

Shift left by 2 units

Reflected over the x-axis

5.

What is the domain for the following function?

a)

All real numbers except 2.

b)

All real number except -2.

c)

All real numbers except 4.

d)

All real numbers.

6.

What is this function called?

a)

Quadratic

b)

Reciprocal

c)

Polynomial

d)

Exponential

7.

What is the horizontal asymptote of the function?

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

a)

$y=-1$

b)

$x=-2$

c)

$y=1$

d)

$x=2$

8.

What is the vertical asymptote of the function?

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

a)

$y=5$

b)

$x=0$

c)

$x=5$

d)

$y=0$

9.

The graph of a reciprocal function is call a:

a)

hyperbola

b)

parabola

c)

cube

d)

absolute value

10.

What are the asymptotes?

a)

x= -1& y = -3

b)

x= 1& y = -3

c)

x= -1& y =3

d)

x= 1& y=3

11.

Which is the graph of the rational equation:

a)

b)

c)

d)

12.

What is the range for the following function?

a)

All real numbers.

b)

All real numbers except for -2.

c)

All real numbers except for 2.

d)

All real numbers exceptt for 4.

13.

Describe the transformations of the function.

a)

Shifted right by 4 units

Shifted down by 7 units

Stretched Vertically

b)

Shifted right by 4 units

Shifted up by 7 units

Stretched Vertically

c)

Shifted right by 4 units

Shifted down by 7 units

Compressed Vertically

d)

Shifted left by 4 units

Shifted down by 7 units

Compressed Vertically

14.

What is the domain of the rational function $f(x) = \frac{1}{x-3}$ ?

a)

All real numbers except $x = 3$

b)

All real numbers

c)

All real numbers except $x = 0$

d)

$x > 3$

15.

Find the x-intercept of the rational function $f(x) = \frac{x-2}{x+3}$ .

a)

$x = 2$

b)

$x = -3$

c)

$x = 3$

d)

$x = -2$

16.

What is the horizontal asymptote of the rational function $f(x)=\frac{3x}{x^2+4}$ ?

a)

$y = 3$

b)

$y = 4$

c)

$y = 0$

d)

$y = 3/4$

17.

What is the domain of the rational function $f(x) = \frac{2}{x^2 - 9}$ ?

a)

All real numbers except $x = 3$ and $x = -3$

b)

All real numbers

c)

All real numbers except $x = 0$

d)

$x > 3$ and $x < -3$

18.

Which of the following is a vertical asymptote of the rational function $f(x)=\frac{5\ \left(x-4\right)}{(x+1)(x-4)}$ ?

a)

$x = 5$

b)

$x = -1$

c)

$x = 4$

d)

$x = 1$ and $x = -4$

19.

Where is the hole in this graph?

a)

x = -3

b)

x = 3

c)

x = 5

d)

None

20.

Which graph matches the function?

a)

A

b)

B

c)

C

d)

D

21.

A rational function will have a horizontal asymptote at $y=0$ when _________.

a)

The degree of the numerator is greater than the degree of the denominator. "Top-heavy"

b)

The degree of the numerator is equal to the degree of the denominator.

c)

The degree of the numerator is less than the degree of the denominator. "Bottom-heavy"

d)

Rational functions can never have horizontal asymptotes at y=0.

22.

What is/are the vertical asymptote(s) of the function?

a)

x = -9

b)

x = 9

c)

x = 3 , x = -3

d)

x = 3

23.

What is/are the vertical asymptote(s) of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

Rational and Reciprocal Functions

Total questions: 23

Worksheet time: 53mins

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