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)? 1. the two functions have the same initial value. 2. the two functions will cross each other on the axis. 3. the two functions have reciprocal output values of each other for any given input value. 4. the two functions have opposite output values of each other for any given input value.

(4) the functions will have opposite output values of each other.

Explanation: A reflection across the x axis is achieved by output value inversion: g(x) = -f(x). Therefore the output values will be opposite, by definition of the reflection, at any point x.

NOTE: The answer (2) is also applicable but not in all cases. The functions will cross each other at the x axis, but only IF the function f(x) ever crosses the x axis. This we do not know and so (2) is true only conditionally.

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