select the correct answer. each statement describes a transformation of the graph of $f(x)=sqrt3{x}$. which…

select the correct answer. each statement describes a transformation of the graph of $f(x)=sqrt3{x}$. which statement correctly describes the graph of $y = f(x - 7)+3$? a. it is the graph of $f$ translated 3 units up and 7 units to the left. b. it is the graph of $f$ translated 7 units down and 3 units to the right. c. it is the graph of $f$ translated 7 units up and 3 units to the right. d. it is the graph of $f$ translated 3 units up and 7 units to the right.

select the correct answer. each statement describes a transformation of the graph of $f(x)=sqrt3{x}$. which statement correctly describes the graph of $y = f(x - 7)+3$? a. it is the graph of $f$ translated 3 units up and 7 units to the left. b. it is the graph of $f$ translated 7 units down and 3 units to the right. c. it is the graph of $f$ translated 7 units up and 3 units to the right. d. it is the graph of $f$ translated 3 units up and 7 units to the right.

Answer

Explanation:

Step1: Recall horizontal - shift rule

For a function $y = f(x - h)$, the graph is shifted $h$ units to the right. Here $h = 7$ in $y=f(x - 7)+3$, so the graph of $y = f(x)$ is shifted 7 units to the right.

Step2: Recall vertical - shift rule

For a function $y=f(x)+k$, the graph is shifted $k$ units up. Here $k = 3$ in $y=f(x - 7)+3$, so the graph of $y = f(x)$ is shifted 3 units up.

Answer:

D. It is the graph of $f$ translated 3 units up and 7 units to the right.