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) in g(x)?

a) The two functions have opposite output values of each other for any given input value.
b) The two functions have the same output values for any given input value.
c) The two functions have opposite input values of each other for any given output value.
d) The two functions have the same input values for any given output value.

Answer 1

For any given input value, an exponential function reflected across the x-axis will have output values that are the exact opposites of the original function, maintaining the same input values but the output values have opposite signs.

Step-by-step explanation:

When an exponential function f(x) is reflected across the x-axis to create the function g(x), the correct statement regarding f(x) and g(x) is option a) The two functions have opposite output values of each other for any given input value.

This reflection across the x-axis means that if f(x) has a value of y for some input x, then g(x) will have a value of -y for the same input x. Therefore, the input values of the functions remain the same, but their output values are negative reciprocals of each other