How to Find Values of Functions from Graphs?

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

Related Topics

• How to Determine Functions?

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 \(x = a\).

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 \(f(4)\). For education statistics and research, visit the National Center for Education Statistics.

Solution: For education statistics and research, visit the National Center for Education Statistics.

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 \(f(2)\).

1. \(\color{blue}{7}\)
2. \(\color{blue}{10}\)