precalculus 12 grade

Question

Given f(x)= 3^x which function represents a reflection across the y-axis and horizontal dilation by 1/2

g(x0= -1/2(3)^x

g(x)= 3^(-2x)

g(x)=-2(3)^x

g(x)=3^(-1.2x)

Answer 1

Reflection across the y-axis means you are reflecting in the x-direction. Consequently, you add a negative to the "x" variable. That would mean the function becomes y = 3^(-x). Horizontal dilations require the reciprocal of the dilation value to be included as a multiplier to the "x". Consequently, a horizontal dilation of 1/2 means "2/1" or "2" be grouped with the "x" as a multiplier.

So, g(x) = 3^(-2x)