Question

consider the graph of the function f(x)= 2^x(picture of graph below) -which statement describes a key feature of function g if g(x)= f(x-4) ?a) y-intercept at (0,1)b) horizontal asymptote of y=0c) horizontal asymptote of y=-4d) y-intercept at (0,3)

Answer 1

Given:

`\begin{gathered} f(x)=2^x \\ g(x)=f(x-4) \\ Hence, \\ g(x)=2^(x-4) \end{gathered}`

The graph showing both functions is shown below;

This indicates a horizontal shift by 4 units to the right.

From the graph, the correct statement that describes the function g(x) is;

The horizontal asymptote is y = 0, because the graph of g(x) does not directly touch y = 0.

Hence, the correct answer is OPTION B.