GOZUNTA
Try it now
All courses Math I · F-IF.5 23 of 59
Relate a function's domain to its graph and to the real-world quantities it describes.

Find the domain of a continuous graph

Problem
Use the continuous graph below to identify its domain.
Coordinate graph showing a closed horizontal segment from x equals negative 2 to x equals 5. Open full size
Your answer
With a free account

Take your practice with you.

Sign in on the web or in the iPhone and iPad app to use the same saved sessions and results.

Create a free account
With paid access

Learn from every walkthrough.

Unlock the complete problem bank and its worked solution walkthroughs, not only the walkthroughs in the starter set.

Compare plans

Hint

Track the x-values that actually appear on the graph.

The domain is the set of all input x-values used by the graph. For continuous graphs, that is usually an interval. For discrete graphs, it is a set of listed values.

Solution walkthrough

01

Read the graph description

\[\text{closed}~\text{segment}~\text{from}~x~=~-2~\text{to}~x~=~5\]

Identify whether the graph is a segment, ray, line, or discrete set of points.

02

Determine the x-values included

\[\text{The}~\text{segment}~\text{includes}~\text{every}~x-\text{value}~\text{from}~-2~\text{to}~5,~\text{and}~\text{both}~\text{endpoints}~\text{are}~\text{closed}.\]

Use endpoint information and the direction of any arrows to describe the domain.

03

Write the domain notation

\[[-2,5]\]

Use interval notation for continuous domains and set notation for discrete domains.

04

State the answer

\[[-2,5]\]

That is the domain of the graph.

+

Another way

  1. Closed endpoints are included with brackets, open endpoints with parentheses, and discrete points with braces.

!

Common mistake

A common mistake is to describe the y-values instead of the x-values when finding the domain.

Coordinate graph showing a closed horizontal segment from x equals negative 2 to x equals 5, showing the domain is negative 2 to 5 inclusive.
[-2,5]