How to Find x and y Values of a Function

You will often be asked to find the $x$ -value when you are given a $y$ -value, or find the $y$ -value when you are given an $x$ -value. To find $x$ -values and $y$ -values, follow these two steps:

Rule

Finding $x$ -values and $y$ -values

To find the $y$ -value:: Insert the $x$ -value you have been given into the function, and calculate the value.
To find the $x$ -value:: Set $f (x)$ equal to the $y$ -value you’ve been given, and solve the equation for $x$ .

Example 1

You have the function $f (x) = 2 x - 3$ . Find the $x$ -value when $f (x) = 2$ , and the $y$ -value when $x = 2$ .

To find $x$ when $f (x) = 2$ :

\begin{array}{l} f (x) & = 2 \\ 2 x - 3 & = 2 \\ 2 x & = 2 + 3 \\ 2 x & = 5 & | \div 2 \\ x & = 2.5 . \end{array}

\begin{array}{l} f (x) = 2 x - 3 & = 2 \\ 2 x & = 2 + 3 \\ 2 x & = 5 & | : 2 \\ x & = 2.5 . \end{array}

Therefore, $x = 2.5$ when $f (x) = 2$ . To find $f (x)$ when $x = 2$ :

\begin{array}{l} f (2) & = 2 \cdot 2 - 3 \\ = 4 - 3 \\ = 1 . \end{array}

f (2) = 2 \cdot 2 - 3 = 4 - 3 = 1 .

Therefore,

f (x) = 1

when

x = 2

Note! To figure out where

f (x)

intersects the axes, this is the procedure:

1.: To find where $f (x)$ intersects the $y$ -axis, you insert 0 for $x$ . So you calculate $f (0)$ , and the answer is the point of intersection between the graph and the $y$ -axis, $(0, f (0))$ .
2.: To find where $f (x)$ intersects the $x$ -axis, you set $f (x) = 0$ . Solve the equation for $x$ , and the answer is the point of intersection between the graph and the $x$ -axis. These points are also called zeros of the function.

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Finding x-values and y-values

Finding $x$ -values and $y$ -values