Question

Which function represents G(x), a reflection of f(x) = 4(1/2)x across the x-axis?

a) G(x) = -4(1/2)x
b) G(x) = -2x
c) G(x) = 4x
d) G(x) = 2x

Answer 1

The function representing a reflection of f(x) = 4(1/2)^x across the x-axis is G(x) = -4(1/2)^x.

Step-by-step explanation:

The question is asking to determine the function G(x), which is a reflection of the function f(x) = 4(1/2)^x across the x-axis. To reflect a function across the x-axis, you multiply the output of the function by -1. Therefore, the reflected function G(x) will be G(x) = -f(x), which in this case is G(x) = -4(1/2)^x.

The correct answer is therefore (a) G(x) = -4(1/2)^x, as this represents the function after it has been reflected over the x-axis, where every y-value of the original function f(x) is multiplied by -1.