Question

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

Explanation:

Step1: Identify horizontal shift

For $f(x-h)^2$, shift right by $h$. Here $h=3$, so shift $f(x)=x^2$ right 3 units.

Step2: Identify vertical scaling

For $a(x-h)^2$, $0<|a|<1$ shrinks vertically. Here $a=\frac{1}{5}$, so shrink by $\frac{1}{5}$.

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 $\frac{1}{5}$.