Question

the function $g(x) = x^2$ is transformed to obtain function $h$: $h(x) = g(x + 7)$. 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 $g$ vertically shifted up 7 units. \\(\bigcirc\\) b. the graph of $h$ is the graph of $g$ horizontally shifted left 7 units. \\(\bigcirc\\) c. the graph of $h$ is the graph of $g$ vertically shifted down 7 units. \\(\bigcirc\\) d. the graph of $h$ is the graph of $g$ horizontally shifted right 7 units.

Explanation:

Step1: Substitute $g(x)$ into $h(x)$

$h(x) = (x+7)^2$

Step2: Analyze horizontal shift rule

For $f(x+a)$, shift left $a$ units.

Answer:

B. The graph of h is the graph of g horizontally shifted left 7 units.