Function:	y = x + 4		f(x) = x2 - 25x
Domain:	x		x
Range:	y		f(x)

Here are examples of possible values for domains and ranges:

Notation	Definition
{1, 3, 5}	Only 1, 3, 5 are members
(-∞, ∞)	All real numbers
(3, ∞)	All real numbers greater than 3
[3, ∞)	All real numbers greater than or equal to 3
(-∞, 0]	All real numbers less than or equal to 0
(-∞, 2) ∪ (3, 10)	All real numbers less than 2 AND all real numbers between 3 and 10

Example 1: Ordered Pairs

Find the domain and range. Give answers in ascending order. Example: {-2, 1, 5} but not {1, -2, 5}
{ (8, 13), (5, -2), (4, 11), (8, 12) }       Domain: Range:

The domain contains all the input values: 8, 5, 4, 8
The range contains all the output values: 13, -2, 11, 12

Remember that duplicate values only need to be listed once.
The answer is Domain: Range:

Example 2: Graphs

Find the domain and range. For ∞, use "inf". Example: Use (-inf, inf) for (-∞, ∞)

Domain: Range:

The domain is all the possible x values and the range is all the possible y values.
From the graph, you can see that x can be all real numbers and y can only be 5.
So the answer is Domain: Range:

Example 3: Expressions

Find the domain and range. For ∞, use "inf". Example: Use (-inf, inf) for (-∞, ∞)
For the union symbol ∪, use capital "U".

f(x) = √x - 1

Domain: Range:

Expressions under radicals must be greater or equal to 0.
To find the domain, solve x - 1 ≥ 0:

x - 1	≥	0
x - 1 + 1	≥	0 + 1
x	≥	1

To find the range, square roots must be greater or equal to 0. Therefore, f(x) ≥ 0.

The answer is Domain: Range: