# How to Find Values of Functions from Graphs?

In a few simple steps, we can find the value of the function from the graph. In this step-by-step guide, you will learn more information about finding values of functions from graphs.

A function in mathematics is represented as a rule, which gives a unique output for each input $$x$$.

## A step-by-step guide tofinding values of functions from graphs

We can find the value of the function from the graph in a few simple steps. Note this example to learn how to find a function from a graph. For example, find the value of a function $$f(x)$$ when $$x = a$$.

1. Draw a vertical line through the value $$a$$ on the $$x$$-axis.
2. Mark the point of intersection of the line $$x = a$$ and the graph of $$f(x)$$.
3. Draw a horizontal line from the point of intersection to the $$y$$-axis.
4. Let the horizontal line meet the $$y$$-axis at $$b$$.

The value of the function $$f(x)$$ at $$x = a$$ is $$b$$. That is, $$f(a) = b$$.

### Finding Values of Functions from Graphs– Example 1:

Use the graph of $$f(x)$$ shown below to find $$f(4)$$.

Solution:

First, draw a vertical line through $$4$$ on the $$x$$-axis. Then mark the intersection of the vertical line $$x = 4$$ and the graph $$f (x)$$. Now draw a horizontal line from the point of intersection to the $$y$$-axis.

So, the value of the function $$f(x)$$ at $$x = 4$$ is $$7$$.

## Exercises forFinding Values of Functions from Graphs

• Use the graph of $$f(x)$$ shown to find $$f(8)$$.
• Use the graph of $$f(x)$$ shown to find $$f(2)$$.
1. $$\color{blue}{7}$$
2. $$\color{blue}{10}$$

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