Determine if the function is one-to-one by noting the functions family to which it belongs and mentally picturing the shape of its graph. f(x) = -|x + 7|-5
A) one-to-one
B) not one-to-one

Question

Quizplus · Accepted Answer

The function belongs to the family of absolute value functions, which typically have V-shaped graphs. The negative sign inside the absolute value ensures that the function is reflected across the x-axis. Therefore, we can mentally picture the graph of the function to be a V-shape with the vertex at (-7,-5) and opening downward. Since the graph does not pass the horizontal line test, the function is not one-to-one. Specifically, two different inputs can produce the same output, such as x = -8 and x = -6, which both produce f(x) = -8.

Determine If the Function Is One-To-One by Noting the Functions