9
QuizMultiple Choice

Reflections of Exponential Functions

Question 9 • High School Math 2 A

How are the two functions f(x) = 0.7(6)x and g(x) = 0.7(6)–x related to each other?

Answer
g
g(x) is the reflection of f(x) over the x-axis.
g
g(x) is the reflection of f(x) over the y-axis.
g
g(x) is the reflection of f(x) over both axes.
g
g(x) and f(x) will appear to be the same function.

Explanation

Replacing x with −x in f gives f(−x) = 0.7(6)^(−x), which is exactly g(x). Replacing x with its opposite reflects a function’s graph across the y-axis, so g is the reflection of f over the y-axis. It is not an x-axis reflection, which would change the output’s sign.

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