Question

Alissa is analyzing an exponential growth function that has been reflected across the y-axis. She states that the domain of the reflected function will change because the input values will be the opposite sign from the reflected function. Simon disagrees with Alissa. He states that if an exponential function is reflected across the y-axis, the domain will still be all real numbers.
Which student is correct and why?

Alissa is correct because the domain will change from negative to positive x-values.
Alissa is correct because a reflection across the y-axis will change the possible input values of the reflected function.
Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.
Neither student is correct.

Answer 1

Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input for an exponential growth function.

Verification of Choice

Let us consider the following exponential growth function.

y = Aeˣ ...........................(1)

This equation changes when it is reflected across the y axis and becomes,

y = Ae⁻ˣ ...........................(2)

Here, the set of all x values for which y is defined is known as the domain of this exponential growth function.

Therefore, the domain of exponential growth function 1 is the set of all real numbers, given by, x ∈ [-∞,∞]

The domain of function 2, which is a reflection of function 1, will also consist entirely of real numbers and will be given by x ∈ [-∞,∞ ]

Therefore, between Alissa and himself, Simon is right when he asserts that even if an exponential growth function is reflected across the y-axis, the domain will still consist only of real values.

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