Determine whether each statement "makes sense" or "does not...

determine whether each statement "makes sense" or "does not make sense" and explain your reasoning.
Regardless of what exponential function I graph, its shape indicates that it always has an inverse function.

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Key Concepts

Inverse Functions

An inverse function reverses the process of the original function, meaning that if you apply the function and then its inverse, you return to your starting value. This concept requires that the function be one-to-one so that each output corresponds to exactly one input.

One-to-One Functions

A one-to-one function is one in which every distinct input yields a distinct output. This property is necessary for a function to have an inverse, and it can be tested using the horizontal line test on a graph.

Exponential Functions

Exponential functions, typically expressed as f(x) = a^x (with a > 0 and a ? 1), are inherently one-to-one because they are strictly increasing (or strictly decreasing if defined in an alternative way). This quality guarantees that each exponential function has an inverse.

Graphical Analysis (Horizontal Line Test)

The horizontal line test is a graphical method used to determine if a function is one-to-one. If every horizontal line intersects the graph of the function at most once, the function is one-to-one and, therefore, possesses an inverse function.

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