Question

use transformations of $f(x)=x^{2}$ to graph the following function.\
\\(\quad g(x)=x^{2}-5\\)\
\\(\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \cdot \cdot \cdot\\)\
what transformation is needed to graph the function $g(x)=x^{2}-5$? choose the correct answer below.\
\\(\bigcirc\\) a. the graph of $f(x)=x^{2}$ should be shifted 5 units down.\
\\(\bigcirc\\) b. the graph of $f(x)=x^{2}$ should be shifted 5 units up.\
\\(\bigcirc\\) c. the graph of $f(x)=x^{2}$ should be shifted 5 units to the right.\
\\(\bigcirc\\) d. the graph of $f(x)=x^{2}$ should be shifted 5 units to the left.

Explanation:

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

Answer:

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