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

To find x when f(x) = 2:

f(x) = 2 2x 3 = 2 2x = 2 + 3 2x = 5 | ÷ 2 x = 2.5.

f(x) = 2x 3 = 2 2x = 2 + 3 2x = 5 | : 2 x = 2.5.

Therefore, x = 2.5 when f(x) = 2.

To find f(x) when x = 2:

f(2) = 2 2 3 = 4 3 = 1.

f(2) = 2 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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