which steps will translate (f(x)=3^{x}) to (g(x)=3^{x + 1}+4)?\nshift (f(x)=3^{x}) one unit up and four…

Explanation:

Step1: Recall horizontal - shift rule

For a function $y = f(x)$, $y=f(x + h)$ is a horizontal shift. If $h>0$, the shift is to the left; if $h < 0$, the shift is to the right. For $f(x)=3^{x}$ and $g(x)=3^{x + 1}$, comparing with $y = f(x+h)$, we have $h = 1$. So, $f(x)$ is shifted 1 unit to the left.

Step2: Recall vertical - shift rule

For a function $y = f(x)$, $y=f(x)+k$ is a vertical shift. If $k>0$, the shift is up; if $k < 0$, the shift is down. For $g(x)=3^{x + 1}+4$, comparing with $y = f(x)+k$, we have $k = 4$. So, the function is shifted 4 units up.

Answer:

Shift $f(x)=3^{x}$ one unit to the left and four units up.