Question

use transformations of the graph of $f(x)=x^{2}$ to determine the graph of the given function.\\
$g(x)=\frac{1}{5}(x - 3)^{2}$\\
\\
b. the graph of $f(x)=x^{2}$ should be horizontally shifted to the right by 3 units and shrunk vertically by a factor of $\frac{1}{5}$.\\
c. the graph of $f(x)=x^{2}$ should be horizontally shifted to the right by 3 units and stretched horizontally by a factor of $\frac{1}{5}$.\\
d. the graph of $f(x)=x^{2}$ should be horizontally shifted to the left by 3 units and stretched horizontally by a factor of $\frac{1}{5}$.\\
use the graphing tool to graph the function.

Explanation:

For a function of the form $g(x)=a(x-h)^2$ derived from $f(x)=x^2$:

1. The term $(x-3)$ indicates a horizontal shift right by 3 units (since $h=3>0$).
2. The coefficient $\frac{1}{5}$ (where $0<|a|<1$) causes a vertical shrink by a factor of $\frac{1}{5}$.

Option B matches these transformations, while options C and D describe incorrect horizontal stretches/shifts.

Answer:

B. The graph of $f(x)=x^2$ should be horizontally shifted to the right by 3 units and shrunk vertically by a factor of $\frac{1}{5}$.