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

Answer:

• C) Simon is correct because even though the input values are opposite in the reflected function, any real number can be an input.

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The exponential growth function has:

• Domain - all real numbers,
• Range - all real numbers excluding zero.

When the function is reflected across the y-axis, we'll have no change to domain or range from what is described above.

Alissa is correct, the input values change to opposite, however the domain stays same - all real numbers.

It means Simon is correct with his statement.

The matching answer choice is C.

Answer 2

Answer:

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

Step-by-step explanation:

Exponential Function

General form of an exponential function:  $f(x)=ab^x$

where:

• a is the initial value (y-intercept)
• b is the base (growth/decay factor) in decimal form
• x is the independent variable
• y is the dependent variable

If b > 1 then it is an increasing function

If 0 < b < 1 then it is a decreasing function

Reflection in the y-axis

$y=f(-x) \implies f(x) \: \textsf{reflected in the} \: y \textsf{-axis}$

As the exponential function is a growth function, b > 1.

If the exponential growth function has been reflected in the y-axis, the x variable is negative:

$\implies f(x)=ab^{-x}$

Regardless whether the initial value $a$ (y-intercept) is positive or negative, the domain of an exponential function is (-∞, ∞) so it is unrestricted.

Therefore, if the function is reflected across the y-axis, the output value for each input value will change, but the domain itself will not change and will still be all real numbers.

Learn more about graph transformations here:

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