Question

the function $g(x) = x^2$ is transformed to obtain function $h$: $h(x) = g(x) - 5$. which statement describes how the graph of $h$ is different from the graph of $g$? \\(\bigcirc\\) a. the graph of $h$ is the graph of $g$ horizontally shifted left 5 units. \\(\bigcirc\\) b. the graph of $h$ is the graph of $g$ vertically shifted down 5 units. \\(\bigcirc\\) c. the graph of $h$ is the graph of $g$ vertically shifted up 5 units. \\(\bigcirc\\) d. the graph of $h$ is the graph of $g$ horizontally shifted right 5 units.

Explanation:

Step1: Recall vertical shift rules

For a function $f(x)$, $f(x)-k$ shifts the graph of $f(x)$ vertically down by $k$ units, where $k>0$.

Step2: Apply rule to given functions

Here, $h(x)=g(x)-5$, so $k=5$. This means the graph of $h(x)$ is the graph of $g(x)$ shifted down 5 units.

Answer:

B. The graph of h is the graph of g vertically shifted down 5 units.