Question

does the graph represent a function that has an inverse?

choose the correct answer below
yes
no

Explanation:

Apply the horizontal line test

A function has an inverse if and only if it is a one-to-one function. Graphically, we determine this using the horizontal line test: if any horizontal line intersects the graph more than once, the function is not one-to-one and does not have an inverse.

Analyze the given graph

The graph shows a downward-opening parabola. A horizontal line drawn through the upper portion of the parabola (below its vertex) will intersect the curve at two distinct points.

Determine the final answer

Since a horizontal line intersects the graph in more than one point, the function is not one-to-one. Therefore, the graph does not represent a function that has an inverse.

Answer:

• Yes
• No (Correct answer)