Question

an exponential function \\(f(x)\\) is reflected across the \\(x\\)-axis to create the function \\(g(x)\\). which is a true statement regarding \\(f(x)\\) and \\(g(x)\\)?

• the two functions have the same initial value.
• the two functions will cross each other on the axis.
• the two functions have reciprocal output values of each other for any given input value.
• the two functions have opposite output values of each other for any given input value.

Explanation:

Define the relationship between the functions

$$ g(x) = -f(x) $$

Analyze the output values

$$ \text{For any input } x, \text{ the output of } g(x) \text{ is the negative (opposite) of } f(x). $$

Evaluate the given statements

$$
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$$

Answer:

• The two functions have the same initial value.
• The two functions will cross each other on the axis.
• The two functions have reciprocal output values of each other for any given input value.
• The two functions have opposite output values of each other for any given input value. (Correct answer)