# 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 \(x\).

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**A step-by-step guide to** **finding 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 \(x = a\).

- Draw a vertical line through the value \(a\) on the \(x\)-axis.
- Mark the point of intersection of the line \(x = a\) and the graph of \(f(x)\).
- Draw a horizontal line from the point of intersection to the \(y\)-axis.
- 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 for** **Finding 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 \(f(2)\).

- \(\color{blue}{7}\)
- \(\color{blue}{10}\)

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