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
