Question

a. the function has an inverse because it passes the vertical line test.
b. the function does not have an inverse because it does not pass the horizontal line test.
c. the function has an inverse because it passes the horizontal line test.
d. the function does not have an inverse because it never crosses the x - axis.

Explanation:

A function has an inverse if and only if it is one-to-one, which is verified by the horizontal line test (no horizontal line intersects the graph more than once). The given graph is strictly increasing, so any horizontal line will cross it at most once, passing the horizontal line test. The vertical line test only confirms it is a function, not that it has an inverse.

Answer:

C. The function has an inverse because it passes the horizontal line test.