Question

graph this function: y = |x| - 5 click to plot the vertex first.

Explanation:

Step1: Find the vertex of the absolute - value function

The general form of an absolute - value function is $y=a|x - h|+k$, and its vertex is $(h,k)$. For the function $y = |x|-5$, which can be written as $y = 1|x - 0|-5$, the vertex is $(0, - 5)$.

Step2: Find points on the left - hand side of the vertex

Let $x=-2$, then $y=| - 2|-5=2 - 5=-3$. So the point is $(-2,-3)$.

Step3: Find points on the right - hand side of the vertex

Let $x = 2$, then $y=|2|-5=2 - 5=-3$. So the point is $(2,-3)$.

Step4: Plot the points

Plot the vertex $(0,-5)$, the point $(-2,-3)$ and $(2,-3)$ and then draw the V - shaped graph of the absolute - value function.

Answer:

Plot the vertex at the point $(0,-5)$, then plot points such as $(-2,-3)$ and $(2,-3)$ and draw the graph of the absolute - value function.