Practice!

Sample Problem

 

This is the graph of the function f(x)=9-(x-2)2. It is not a one-to-one function. What restrictions do we have to put on the domain so that the resulting function is one-to-one? (there may be more than one correct answer, so pick all answers that apply)

 

(-∞, 2)

(0, 4)

(-∞, 0)

(2, ∞)

(-5, 3)

Solution

In order to find out which restrictions will make this function one-to-one, apply each of the restrictions on the domain intervals and see if the restricted function passes the horizontal line test. (-∞, 2), (-∞, 0), and (2,∞) all make this function one-to-one since after setting the aforementioned restrictions, no horizontal line intersects the graph of f at more than one point.

On the other hand, restricting the function to the interval (0,4) and also to the interval (-5, 3) still allows a horizontal line to pass through the graph of f at more than one point.