Question

does the graph represent a function that has an inverse function?
choose the correct answer below.
yes
no

Explanation:

Apply the horizontal line test

Using the Horizontal Line Test knowledge point

$$ \text{A function has an inverse if and only if it is one-to-one.} $$

$$ \text{If any horizontal line intersects the graph more than once, it is not one-to-one.} $$

Analyze the given graph

Using the One-to-One Functions knowledge point

$$ \text{The graph is a cubic-like curve with a local minimum and a local maximum.} $$

$$ \text{A horizontal line drawn through the peaks/valleys intersects the curve at three distinct points.} $$

$$ \text{Since it fails the horizontal line test, the function does not have an inverse.} $$

Answer:

• Yes
• No (Correct answer)