Question

3 multiple answer 25 points

1. the graph of $p(x) = x^2$ was stretched horizontally to create the function $h(x)$. which of the following could represent the function $h(x)$?

select all the correct answers.
$h(x) = 3.5x^2$
$h(x) = (0.2x)^2$
$h(x) = (x - 3.7)^2$
$h(x) = (0.45x)^2$
$h(x) = (x + 4.8)^2$
$h(x) = 7.8x^2$

Explanation:

Step1: Recall horizontal stretch rule

For a parent function $p(x)$, a horizontal stretch by a factor of $\frac{1}{k}$ (where $0<|k|<1$) gives $h(x)=p(kx)$.

Step2: Analyze each option

• $h(x)=3.5x^2$: Vertical stretch, not horizontal.
• $h(x)=(0.2x)^2$: $k=0.2<1$, horizontal stretch.
• $h(x)=(x-3.7)^2$: Horizontal shift right, not stretch.
• $h(x)=(0.45x)^2$: $k=0.45<1$, horizontal stretch.
• $h(x)=(x+4.8)^2$: Horizontal shift left, not stretch.
• $h(x)=7.8x^2$: Vertical stretch, not horizontal.

Answer:

B. $h(x) = (0.2x)^2$, D. $h(x) = (0.45x)^2$