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 $g$ horizontally shifted right 5 units. \\(\bigcirc\\) d. the graph of $h$ is the graph of $g$ vertically shifted up 5 units.

Explanation:

For a function transformation of the form $h(x) = g(x) + k$, when $k$ is negative, the graph of $g(x)$ is shifted vertically downward by $|k|$ units. Here, $h(x) = g(x) - 5$, so $k=-5$, meaning the graph shifts down 5 units. Horizontal shifts involve modifying the input $x$ (e.g., $g(x-h)$), which is not the case here.

Answer:

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