13
QuizMultiple Choice

Exponential and Logarithmic Functions: Part One — Test

Question 13 • Advanced Algebra: Concepts and Connections

Which statement could be used to explain why the function h of x is equal to x cubed has an inverse relation that is also a function?

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

Explanation

A function has an inverse relation that is also a function when the original function is one-to-one. The horizontal line test checks whether each horizontal line intersects the graph at most once. Since h(x) = x³ passes that test, its inverse relation is a function. The correct statement is that the graph of h(x) passes the horizontal line test.

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