Question

Each statement describes a transformation of the graph of f(x)=3 square root of 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 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 1

Step-by-step explanation:

The correct statement that describes the graph of y = f(x − 7) + 3 is:

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

Step-by-step explanation:

Starting with the original function f(x) = 3√x, the given transformation y = f(x − 7) + 3 indicates that the graph has undergone two transformations: a horizontal translation (shifting) of 7 units to the right and a vertical translation of 3 units up.

The function f(x − 7) represents a horizontal translation of 7 units to the right, moving the entire graph horizontally. Then, adding +3 to the function results in a vertical translation of 3 units up.

Therefore, the correct statement is that the graph of y = f(x − 7) + 3 is the graph of f translated 3 units up and 7 units to the right.