Question

Consider the graph of the function f(x)=2^x

Which statement describes a key feature of function g if g(x)=f(x-4)

Answer 1

• A. Horizontal asymptote of y = 0

Explanation:

Given function:

• f(x) = 2ˣ

And the function g(x):

• g(x) = f(x - 4)

g(x) is the horizontal shift of f(x) 4 units right.

It has a different y-intercept but same asymptote with f(x), which is y = 0 as the exponential function never reaches zero and never negative. Hence option B is incorrect.

The y-intercept of f(x) is (0, 1) but the y-intercept of g(x) is smaller:

• g(0) = 2⁻⁴ = 1/16

So we are left with option A