Question

use the graph $y = f(x)$ to graph the given function.
$y = \frac{1}{7}f(x)$

Explanation:

Step1: Identify key points of $f(x)$

The vertices of $y=f(x)$ are: $(-7, 0)$, $(0, 7)$, $(7, 0)$

Step2: Apply vertical compression factor

Multiply each $y$-coordinate by $\frac{1}{7}$:
For $(-7, 0)$: $y = \frac{1}{7} \times 0 = 0$, new point $(-7, 0)$
For $(0, 7)$: $y = \frac{1}{7} \times 7 = 1$, new point $(0, 1)$
For $(7, 0)$: $y = \frac{1}{7} \times 0 = 0$, new point $(7, 0)$

Step3: Plot and connect new points

Draw line segments between $(-7, 0)$, $(0, 1)$, and $(7, 0)$.

Answer:

The graph of $y=\frac{1}{7}f(x)$ is a vertical compression of $y=f(x)$ by a factor of $\frac{1}{7}$, with vertices at $(-7, 0)$, $(0, 1)$, and $(7, 0)$, connected by straight line segments.