Question

Which statement best describes the effect of replacing the function f(x) = 2^x − 2 with the function g(x) = 2^x + 3?

The graph shifts 1 units left.
The graph shifts 5 units left.
The graph shifts 1 unit right.
The graph shifts 3 units right.

Answer 1

The graph shifted by 5 units

Answer 2

Answer:

Option B - The graph shifts 5 units left.

Step-by-step explanation:

Given : Equation 1- $f(x)=2^{x-2}$

after replacing the function we get, equation 2-  $g(x)=2^{x+3}$

The function  $f(x)=2^{x-2}$ is transformed to g(x) when we add 5 in the x value

$f(x)=2^{x-2}$

⇒ $f(x+5)=2^{x-2+5}$

⇒ $f(x+5)=2^{x+3}=g(x)$

and when we add something in the x value then the graph shifted to left by that unit.

mathematically we can write,  

f(x)→ f(x+b) →  f(x) shift left with b units

Therefore, the graph shifts 5 unit to the left

Hence, option B is correct