9
QuizMultiple Choice

Exponential and Logarithmic Functions: Part One — Test

Question 9 • Advanced Algebra: Concepts and Connections

Which statement could be used to explain why f of x is equal to 2 x minus 3 has an inverse relation that is a function?

Answer
A
The graph of f of x passes the vertical line test.
B
f of x is not a function.
C
The graph of the inverse of f of x passes the horizontal line test.
D
f of x is a one-to-one function.

Explanation

The function f(x) = 2x − 3 is one-to-one: different input values produce different output values because its slope is nonzero. A function has an inverse relation that is also a function precisely when the original function is one-to-one. Therefore, the statement that f of x is a one-to-one function explains why its inverse relation is a function.

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