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

Option B - The graph shifts 5 units left.

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