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)? A. The the functions have the same initial value. B. The two functions will cross each other on the axis. C. The two functions have reciprocal output values of each other for any given output value. D. The two functions have opposite output values of each other for any given input value.

Answer 1

The answer is D

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Answer 2

D. The two functions have opposite output values of each other for any given input value.

Explanation:

The reflect function will have opposite output values than the original one, because reflection across the x-axis means that y-values will be with the opposite sign. All positive y-values in the original function will have negative values in the reflected one, and all negative y-values in the original will have positive values in the reflected.

The opposite values are just seen in the output, because those belong to y-axis, all x-axis values remain the same, which are input values. You can see this in the image attached, look for the horizontal reflection. That mirror effect across the x-axis is because the y-values are opposite.