Question

use transformations of $f(x)=x^2$ to graph the following function. \\( g(x)=x^2 - 5 \\) \\( \dots \\) answer below. \\( \boldsymbol{\text{a.}} \\) the graph of $f(x)=x^2$ should be shifted 5 units down. \\( \boldsymbol{\text{b.}} \\) the graph of $f(x)=x^2$ should be shifted 5 units up. \\( \boldsymbol{\text{c.}} \\) the graph of $f(x)=x^2$ should be shifted 5 units to the right. \\( \boldsymbol{\text{d.}} \\) the graph of $f(x)=x^2$ should be shifted 5 units to the left. \\( \text{use the graphing tool to graph the function.} \\) click to enlarge graph

Explanation:

For a function transformation of the form $g(x) = f(x) - k$ where $k>0$, the graph of the parent function $f(x)$ is shifted vertically downward by $k$ units. Here, $g(x)=x^2 -5 = f(x)-5$, so the shift is 5 units down.

Answer:

A. The graph of $f(x)=x^{2}$ should be shifted 5 units down.