Finding an Output of a Function from its Graph

 Algebra 1 Skills Practice

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

  • 00:04 Finding an output of a…
  • 01:01 Finding an output of a…
  • 01:47 Finding an output of a…
  • 02:32 Finding an output of a…
Jump to a specific example
Dana Hansen, Jenna Feldman
  • Instructors
    Dana Hansen

    Dana has taught high school mathematics for over 9 years. She has a masters in mathematics education from CU Denver. She is certified to teach both mathematics and physics in both Colorado as well as Iowa. She loves getting outdoors as much as possible hopefully with her two dogs. Dana has tutored with study.com for over a year, and loves the opportunity to work one on one with students to help them develop their content knowledge.

  •  
    Jenna Feldman

    Jenna Feldman has been a High School Mathematics teacher for ten years. She has worked with students in courses including Algebra, Algebra 2, Precalculus, Geometry, Statistics, and Calculus. She has a bachelor’s degree in mathematics from the University of Delaware and a Master of Education degree from Wesley College.

Example Solutions Practice Questions

How to Find an Output of a Function from its Graph

Step 1: Identify the {eq}x{/eq}-value of the point we are looking for. The number inside the parentheses, or the input of the function, is the {eq}x{/eq}-value of the point we need to find.

Step 2: Find the point on the graph where {eq}x{/eq} is equal to the value identified in the previous step. Determine the coordinates of this point.

Step 3: The {eq}y{/eq}-value of the point identified in the previous step is the output asked for in the problem.

How to Find an Output of a Function from its Graph Vocabulary

Input of a graph: The input values for a graph of a function are the {eq}x{/eq}-values of points on the graph. In function notation, f(x), the input is the value inside the parentheses.

Output of a graph: The output values for a graph of a function are the {eq}y{/eq}-values of the points on the graph. In function notation, the output is represented as f(x), where x is the input.

So, let's try using these steps and definitions to find an output of a function from its graph, in the following two examples.

How to Find an Output of a Function from its Graph: Example 1

Using the graph of the function {eq}f(x){/eq} shown below, find {eq}f(4){/eq}.

Graph for first example

Step 1: Identify the {eq}x{/eq}-value of the point we are looking for. The number inside the parentheses, or the input of the function, is the {eq}x{/eq}-value of the point we need to find.

We are asked to find {eq}f(4){/eq}. The number inside the parentheses, or the input of the function, is 4, which means we are looking for a point on the graph with an {eq}x{/eq}-value that is equal to 4.

Step 2: Find the point on the graph where {eq}x{/eq} is equal to the value identified in the previous step. Determine the coordinates of this point.

We need to follow the graph until we get to {eq}x=4. {/eq}


Point for the first example


The coordinates of this point are {eq}(4,5) {/eq}.

Step 3: The {eq}y{/eq}-value of the point identified in the previous step is the output asked for in the problem.

The {eq}y{/eq}-coordinate of the point from the previous step is 5. Therefore:

$$\boxed{f(4)=5} $$

How to Find an Output of a Function from its Graph: Example 2

Using the graph of the function {eq}f(x){/eq} shown below, find {eq}f(-2){/eq}.

Graph for second example

Step 1: Identify the {eq}x{/eq}-value of the point we are looking for.

We are looking for a point on the graph with an {eq}x{/eq}-value that is -2.

Step 2: Determine the coordinates of the point we need.

The coordinates of this point are {eq}(-2,8) {/eq}.

Step 3: The {eq}y{/eq}-value of the point identified in the previous step is the output asked for in the problem.

The {eq}y{/eq}-value of the point (-2,8) is 8, so:

$$\boxed{f(-2)=8} $$

Recently updated on Study.com

Support