Question

use transformations of the graph of $f(x)=x^{2}$ to determine the graph of the given function.\\(g(x)=(x + 3)^{2}\\)\\(\\)\\(\\)what transformation is needed to graph the function $g(x)=(x + 3)^{2}$? choose the correct answer below.\\(\\)\\(\\)\\(\bigcirc\\) a. the graph of $f(x)=x^{2}$ should be shifted 3 units down.\\(\\)\\(\bigcirc\\) b. the graph of $f(x)=x^{2}$ should be shifted 3 units to the left.\\(\\)\\(\bigcirc\\) c. the graph of $f(x)=x^{2}$ should be shifted 3 units up.\\(\\)\\(\bigcirc\\) d. the graph of $f(x)=x^{2}$ should be shifted 3 units to the right.

Explanation:

For a parent function $f(x)=x^2$, a transformed function of the form $f(x+h)$ represents a horizontal shift. When $h>0$, the graph shifts left by $h$ units. Here, $g(x)=(x+3)^2 = f(x+3)$, so $h=3$, meaning the graph shifts left 3 units.

Answer:

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