Final answer:
The statement explaining why the function h(x) = x³ has an inverse that is also a function is that the graph of h(x) passes the horizontal line test, ensuring the inverse passes the vertical line test.
Therefore, the correct answer is: option "The graph of h(x) passes the horizontal line test."
Step-by-step explanation:
The statement that could be used to explain why the function h(x) = x³ has an inverse relation that is also a function is: "The graph of h(x) passes the horizontal line test."
This is because for a function to have an inverse that is also a function, every horizontal line must intersect the graph of the function at most once, ensuring that the inverse relation will pass the vertical line test.
For example, if we take the function h(x) = x³, the graph of this function is a curve that passes through every horizontal line exactly once, which means its inverse will pass through every vertical line once as well.
Therefore, the inverse relation is also a function. This property is generally true for cubic functions like x³, and it is why the inverse of h(x) = x³ is also a function.