Topics
4. Functions and Relations
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Middle Years

4.04 Domain and range

Lesson
Worksheet
Practice
Worksheet
Domain and range
1

For each relation below:

i
State the domain.
ii
State the range.
iii
State whether it is a function.
a

\left\{\left(16, 14\right), \left(8, 28\right), \left( - 15 , 14\right), \left( - 20 , - 28 \right)\right\}

b
x77853
y19326
c
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
y
d
1
2
3
4
5
6
7
x
1
2
3
4
5
6
7
y
e
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
f
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
2

Consider the function graphed:

a

State the domain.

b

State the range.

-6
-4
-2
2
4
6
x
-6
-4
-2
2
4
6
y
3

Consider the graph of y = \sqrt[3]{ - x }:

a

State the domain.

b

State the range.

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
4

The function f \left(x\right) = \sqrt{x + 1} has been graphed below:

a

State the domain.

b

Is there a value of x in the domain that can produce a function value of - 2?

-4
-3
-2
-1
1
2
3
4
x
-4
-3
-2
-1
1
2
3
4
y
5

Consider the graph of the function y = f \left( x \right):

a

State the maximum value.

b

State the range.

c

State the domain.

-10
-8
-6
-4
-2
2
x
-8
-6
-4
-2
2
4
6
8
10
12
14
16
y
6

The function y = \sqrt{x} has a domain of x \geq 0 and a range of y \geq 0. State the domain and range of y = \sqrt{x} - 2.

7

State the natural domain of the the following functions:

a

f \left( x \right) = \dfrac{1}{\sqrt{x}}

b
f \left( x \right) = \dfrac{1}{\sqrt{x + 4}}
c
f \left( x \right) = \dfrac{1}{\sqrt{5 - x}}
Interval notation
8

State the domain of the following functions using interval notation:

a
f \left( x \right) = \dfrac{1}{x + 5}
b
f \left( x \right) = \dfrac{x + 8}{4 - x}
9

For each graph below, state the following using interval notation.

i

The domain

ii

The range

a
-7
-6
-5
-4
-3
-2
-1
1
x
-4
-3
-2
-1
1
2
3
4
y
b
-1
1
2
3
4
5
6
7
8
9
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
c
-8
-7
-6
-5
-4
-3
-2
-1
1
2
x
-5
-4
-3
-2
-1
1
2
3
4
5
y
d
-2
2
4
6
8
10
x
-6
-4
-2
2
4
6
y
e
-2
2
4
6
8
10
x
-6
-4
-2
2
4
6
y
f
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
g
-6
-4
-2
2
4
6
x
-6
-4
-2
2
4
6
y
h
-8
-6
-4
-2
2
4
6
8
x
-8
-6
-4
-2
2
4
6
8
y
10

Use the graph of f to find:

a

The domain.

b

The range.

c

f \left( 0 \right)

d

f \left( 1 \right) - f \left( 7 \right)

-5
-4
-3
-2
-1
1
2
3
4
5
6
7
x
-4
-2
2
4
6
8
10
12
14
16
y
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