Question

move at least one of the 9 guide points below to complete the graph of (y = -\frac{1}{4}|x|). moving the red points changes the vertical stretch or compression. moving the blue point shifts the function left/right/up/down. click the buttons below to start over or reflect over the x - axis. reset reflect over x - axis

Explanation:

Step1: Analyze the function

The function is $y =-\frac{1}{4}|x|$. The negative sign reflects the graph of $y = \frac{1}{4}|x|$ over the x - axis, and the $\frac{1}{4}$ compresses the graph of $y = |x|$ vertically by a factor of $\frac{1}{4}$.

Step2: Find key points

For $y = |x|$, key points are $(0,0),(1,1),(- 1,1)$. For $y=-\frac{1}{4}|x|$, when $x = 0$, $y = 0$; when $x = 1$, $y=-\frac{1}{4}$; when $x=-1$, $y =-\frac{1}{4}$.

Step3: Adjust the graph

Move the red points to change the vertical compression to match the factor of $\frac{1}{4}$ and reflect the graph over the x - axis due to the negative sign.

Answer:

Move the red points to adjust the vertical compression to a factor of $\frac{1}{4}$ and use the "Reflect over x - axis" button to correct the orientation of the graph.