Question

The function f(x)=2^x and g(x)= f(x+k). If k =-5, what can be concluded about the graph of g(x)?

Answer 1

Answer:

The graph of g(x) is the graph of f(x) shifted 5 units right.

Step-by-step explanation:

Horizontal shift:

The parent function y = f(x), then the transformation  y = f(x+h) is horizontal shift either right or left.

If h < 0, then the shift is right by h units

if h >0 then, the  shift is left by h units

If a parent function

Given the function

$f(x) = 2^x$

and

$g(x) = f(x+k)$

⇒$g(x) =2^{x+k}$

If k = -5 then;

$g(x) = 2^{x-5}$

By definition :

k = -5 < 0

⇒the graph of g(x) is the graph of f(x) shifted 5 units right.

Answer 2

The graph of $g(x)$ is the graph of $f(x)$ shifted 5 units right.