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PCAT Quantitative Reasoning – Inverse Function Graph

What is the equation for the inverse of the function shown below?

A. y = 4x + 8
B. x/4 – 2
C. x/4 + 2
D. y = 2x + 4

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A is correct. The first task is to find the equation for the function shown. Recall that the equation for a line in slope-intercept form is y = mx + b, where m is the slope and b is the y value of the y-intercept. Let’s identify two points on the line, such as (0, –2) and (8, 0), to determine the slope:

We can also see that the line intersects the y-axis at (0, –2), so b = –2. Therefore, the equation for the line shown must be: y = 1/4 x – 2. To determine the inverse function, let’s swap x and y and then solve for x:

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