Domain and Range of Functions

In this lesson we will at the domain and range of functions

The domain of a function is the set of all the allowable values that can be used as the input to the function.

The range of a function is the set of values that can be obtained as the output of the function.

Example:

Find the domain and range of

Solution:

For f(x) to be a real number

1 – x² ≥ 0
x² ≤ 1
–1 ≤ x ≤ 1

Therefore, the domain is –1 ≤ x ≤ 1

The smallest value for f(x) is when x = 1 or –1

The largest value for f(x) is when x = 0

Therefore, the range is 0 ≤ y ≤ 1

Example:

Find the domain of

Solution:

If (x – 2)(x + 5) = 0 then f(x) would be undefined.

For (x – 2)(x + 5) = 0, either x = 2 or x = –5

Therefore, the domain consist of all real numbers, except 2 and –5

Videos

Domain and Range
An important part of understanding functions is understanding their domain and range. Domain and range are all the possible x-values and y-values of the function, and can often be described easily by looking at a graph. In order to grasp domain and range, students must understand how to determine if a relation is a function and interpreting graphs.

Reading Domain and Range of a Relation From a Graph

Finding the Domain of a Function

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