Question

Which statement could be used to explain why the function h(x) = x^3 has an inverse relation that is also a function?

A) The graph of h(x) passes the vertical line test.
B) The graph of the inverse of h(x) is a vertical line.
C) The graph of the inverse of h(x) passes the horizontal line test.
D) The graph of h(x) passes the horizontal line test.

Answer 1

The function h(x) = x^3 has an inverse relation that is also a function because the graph of h(x) passes the vertical line test.

Step-by-step explanation:

The correct statement that could be used to explain why the function h(x) = x^3 has an inverse relation that is also a function is option A) The graph of h(x) passes the vertical line test.

The vertical line test is a test used to determine if a graph represents a function. If every vertical line that intersects the graph crosses the graph at only one point, then the graph represents a function. In the case of the function h(x) = x^3, every vertical line intersects the graph at only one point, which means that the graph passes the vertical line test and therefore the inverse relation is also a function.