Question

describe the transformation from the graph of f to the graph of h. 9. f(x) = 8x + 3; h(x) = f(4x) 10. f(x) = -3x - 6; h(x) = \frac{2}{3}f(x)

Explanation:

Step1: Solve for h(x) in Q9

Substitute $4x$ into $f(x)$:
$h(x)=f(4x)=8(4x)+3=32x+3$

Step2: Identify Q9 transformation

Compare $f(x)=8x+3$ and $h(x)=32x+3$. The coefficient of $x$ is scaled by 4, so this is a horizontal compression.

Step3: Solve for h(x) in Q10

Substitute $f(x)$ into $\frac{2}{3}f(x)$:
$h(x)=\frac{2}{3}(-3x-6)=\frac{2}{3}(-3x)+\frac{2}{3}(-6)=-2x-4$

Step4: Identify Q10 transformation

Compare $f(x)=-3x-6$ and $h(x)=-2x-4$. All terms are multiplied by $\frac{2}{3}$, so this is a vertical compression.

Answer:

1. The graph of $h(x)$ is a horizontal compression of the graph of $f(x)$ by a factor of $\frac{1}{4}$.
2. The graph of $h(x)$ is a vertical compression of the graph of $f(x)$ by a factor of $\frac{2}{3}$.