Free Printable Functions and Their Graphs

1.

Which equation corresponds to the graph below.

a)

$k\left(x\right)=3\cdot\left(\frac{1}{2}\right)^x+4$

b)

$f\left(x\right)=3\cdot2^x+4$

c)

$f\left(x\right)=3\cdot2^x-4$

d)

$m\left(x\right)=3\left(\frac{1}{2}\right)^2-4$

2.

Given the equation below determine the asymptote.

a)

(0, 1)

b)

(0, 3)

c)

x= 0

d)

y = 0

3.

Determine the asymptote of the equation below:

g\left(x\right)=4\cdot2^x+3

a)

y = 4

b)

y = 2

c)

y = 3

4.

Identify which functions are exponential.

a)

f(x) = 2x - 5

b)

g(x) = 3^x

c)

k(x) = 3x⁴ - 6x + 9

d)

k\left(x\right)=3\cdot\left(\frac{1}{2}\right)^x

5.

Sketch the graph of each function.

a)

b)

c)

d)

6.

Find the interval(s) of increase of the graph shown.

a)

(-6, -4)

b)

(-4, -2)

c)

(-2, 2)

d)

(2, 5)

e)

(5, 6)

7.

The graph of the rational function is shown to the left. What is the equation that represents this function?

a)

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

b)

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

c)

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

d)

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

8.

What are the restrictions on the domain of the following function?

a)

$x\ne4$ only

b)

$x\ne0$

c)

$x\ne5$ only

d)

$x\ne-4$ and $x\ne5$

9.

Where is there a hole (point or removable discontinuity) in the graph of the following function?

a)

$x=-4$ only

b)

$x=0$ only

c)

$x=5$ only

d)

$x=4$ only

10.

Find the horizontal asymptote for the following function.

a)

$y=\frac{5}{8}$

b)

$y=\frac{8}{5}$

c)

$y=0$

d)

no horizontal asymptote

11.

Find the horizontal asymptote for the following function.

a)

$y=\frac{3}{4}$

b)

no horizontal asymptote

c)

$y=0$

d)

$y=\frac{4}{3}$

12.

Find the horizontal asymptote for the following function.

a)

$y=\frac{9}{4}$

b)

no horizontal asymptote

c)

$y=0$

d)

$y=\frac{4}{9}$

13.

The horizontal asymptote in the graph of $f\left(x\right)=\frac{\left(5x+3\right)\left(2x-9\right)}{x\left(2x+1\right)}$ is represented by which equation?

a)

$y=5$

b)

$y=0$

c)

no horizontal asymptote

d)

$y=10$

14.

The graph of the rational function is shown to the left. What is the equation that represents this function?

a)

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

b)

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

c)

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

d)

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

15.

The graph of the rational function is shown to the left. What is the equation that represents this function?

a)

$f\left(x\right)=\frac{4\left(x-2\right)\left(x-6\right)}{\left(x-6\right)}$

b)

$f\left(x\right)=\frac{4\left(x-2\right)}{\left(x-6\right)\left(x-6\right)}$

c)

$f\left(x\right)=\frac{\left(x-6\right)}{4\left(x-6\right)\left(x-2\right)}$

d)

$f\left(x\right)=\frac{4\left(x-6\right)}{\left(x-6\right)\left(x-2\right)}$

16.

Is the equation linear, exponential or neither?

a)

Linear

b)

Exponential

c)

Neither

17.

What type of function is y = 7(5/4)^x?

a)

Exponential Growth

b)

Exponential Decay

c)

Linear

d)

None of the above

18.

What is g(7) if:

a)

-17

b)

-13

c)

13

d)

17

19.

Using the pictured graph, what is f(-3)?

a)

-3

b)

-1

c)

1

d)

3

20.

a)

A

b)

B

c)

C

d)

D

Functions and Their Graphs

Total questions: 20

Worksheet time: 20mins

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