Question

move at least one of the 9 guide points below to complete the graph of (y = 5|x|-3). 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 $y = 5|x|-3$. The parent - function of an absolute - value function is $y = |x|$. The coefficient 5 in front of $|x|$ causes a vertical stretch by a factor of 5, and the subtraction of 3 shifts the graph down by 3 units.

Step2: Find the vertex

For the absolute - value function $y=a|x - h|+k$, the vertex is at the point $(h,k)$. In the function $y = 5|x|-3$, $h = 0$ and $k=-3$, so the vertex should be at the point $(0, - 3)$. Currently, the vertex in the graph is at $(0,0)$. So, move the blue point (which shifts the function up/down/left/right) down 3 units to the point $(0,-3)$.

Answer:

Move the blue point to the point $(0, - 3)$.