Question

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.

Explanation:

Step1: Recall Function Translation Rules

For a function \( y = f(x - h) + k \), the graph of \( f(x) \) is translated \( h \) units to the right (if \( h>0 \)) and \( k \) units up (if \( k>0 \)).

Step2: Identify \( h \) and \( k \) in \( y = f(x - 7)+3 \)

Here, \( h = 7 \) (so translation 7 units right) and \( k = 3 \) (so translation 3 units up).

Answer:

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