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 ) vertically shifted down 7 units.( \bigcirc ) c. the graph of ( h ) is the graph of ( g ) horizontally shifted right 7 units.( \bigcirc ) d. the graph of ( h ) is the graph of ( g ) horizontally shifted left 7 units.

Explanation:

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

Given $g(x)=x^2$, substitute into $h(x)=g(x+7)$:
$h(x)=(x+7)^2$

Step2: Analyze horizontal shift rule

For a function $f(x)$, $f(x+a)$ shifts left by $a$ units.
Here, $a=7$, so shift left 7 units.

Answer:

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