Question

use transformations of the graph of $f(x)=x^2$ to determine the graph of the given $g(x)=(x + 3)^2$ \
a. the graph of $f(x)=x^2$ should be shifted 3 units down.\
b. the graph of $f(x)=x^2$ should be shifted 3 units to the left.\
c. the graph of $f(x)=x^2$ should be shifted 3 units up.\
d. the graph of $f(x)=x^2$ should be shifted 3 units to the right.\
use the graphing tool to graph the function.

Explanation:

Step1: Recall horizontal shift rule

For $f(x) = x^2$, $f(x + h)$ shifts left by $h$ units.

Step2: Match to given function

Here, $g(x) = (x+3)^2 = f(x+3)$, so $h=3$.

Answer:

B. The graph of $f(x)=x^2$ should be shifted 3 units to the left.