Which function represents a reflection of f(x) = (4)x across the y-axis? g(x) = g(x) = (4)x g(x) = (4)-x g(x) = (4)–x

Question

This is a problem that i am having trouble with. i just dont understand reflections of exponential functions.

Answer 1

Kaleb,

 

You can think of reflections as rotations of 180 degrees about the specified axis.

 

Thus reflecting any function y = f(x), not just an exponential:

 

About the y-axis, keeps y the same but flips the sign of x to -x. so y = f(-x) is the reflected function.

 

About the x-axis, keeps x the same but flips the sign of y to -y so -y = f(x) or y = - f(x).

 

So in your example of reflecting f(x) = 4x about the y-axis:

y = 4(-x) = - 4x