test yourself! practice tool\nthe function $g(x)=f(x + 3)+2$. which of the following is true of the graph of…

test yourself! practice tool\nthe function $g(x)=f(x + 3)+2$. which of the following is true of the graph of $g(x)$?\no the graph of $g(x)$ is shifted 3 units to the right and 2 units above the graph of $f(x)$.\no the graph of $g(x)$ is shifted 3 units to the left and 2 units above the graph of $f(x)$.\no the graph of $g(x)$ is shifted 3 units to the right and 2 units below the graph of $f(x)$.\no the graph of $g(x)$ is shifted 3 units to the left and 2 units below the graph of $f(x)$.

test yourself! practice tool\nthe function $g(x)=f(x + 3)+2$. which of the following is true of the graph of $g(x)$?\no the graph of $g(x)$ is shifted 3 units to the right and 2 units above the graph of $f(x)$.\no the graph of $g(x)$ is shifted 3 units to the left and 2 units above the graph of $f(x)$.\no the graph of $g(x)$ is shifted 3 units to the right and 2 units below the graph of $f(x)$.\no the graph of $g(x)$ is shifted 3 units to the left and 2 units below the graph of $f(x)$.

Answer

Explanation:

Step1: Recall horizontal shift rule

For a function $y = f(x + h)$, if $h>0$, the graph shifts $h$ units to the left. Here $h = 3$ in $g(x)=f(x + 3)+2$, so the graph of $f(x)$ shifts 3 units to the left.

Step2: Recall vertical shift rule

For a function $y=f(x)+k$, if $k > 0$, the graph shifts $k$ units up. Here $k = 2$ in $g(x)=f(x + 3)+2$, so the graph of $f(x)$ shifts 2 units up.

Answer:

The graph of $g(x)$ is shifted 3 units to the left and 2 units above the graph of $f(x)$.