graph the equation.\ny = 3|x|

Explanation:

Step1: Consider cases for absolute - value.

When (x\geq0), (y = 3x). When (x<0), (y=-3x).

Step2: Find key points for (x\geq0).

Let (x = 0), then (y=3\times0 = 0); let (x = 1), then (y = 3\times1=3); let (x = 2), then (y=3\times2 = 6).

Step3: Find key points for (x<0).

Let (x=-1), then (y=-3\times(-1)=3); let (x = - 2), then (y=-3\times(-2)=6).

Step4: Plot the points and draw the graph.

Plot ((0,0)), ((1,3)), ((2,6)), ((-1,3)), ((-2,6)) and connect them with straight - line segments. The graph is a "V" - shaped graph with the vertex at the origin ((0,0)) opening upwards.

Answer:

The graph of (y = 3|x|) is a "V" - shaped graph with vertex at ((0,0)) opening upwards, passing through points such as ((-2,6)), ((-1,3)), ((0,0)), ((1,3)), ((2,6)) etc.