Question

graph the following absolute value expression:
$y = 3|-x|$
show your work here

Explanation:

Step1: Simplify absolute value term

Recall that $|-x| = |x|$, so the equation simplifies to:
$y = 3|x|$

Step2: Define piecewise form

Split the absolute value into two cases:
For $x \geq 0$: $y = 3x$
For $x < 0$: $y = 3(-x) = -3x$

Step3: Identify key points

• Vertex (when $x=0$): $y=3|0|=0$, so point $(0,0)$
• For $x>0$: Choose $x=2$, $y=3(2)=6$, point $(2,6)$; $x=4$, $y=3(4)=12$, point $(4,12)$
• For $x<0$: Choose $x=-2$, $y=3|-2|=6$, point $(-2,6)$; $x=-4$, $y=3|-4|=12$, point $(-4,12)$

Step4: Plot and connect points

Draw a V-shaped graph with vertex at $(0,0)$, rising with slope $3$ for $x>0$, and rising with slope $3$ for $x<0$ (equivalent to slope $-3$ for the left piece from the vertex).

Answer:

The graph is a V-shaped curve with vertex at $(0,0)$, passing through points like $(-2,6)$, $(2,6)$, $(-4,12)$, $(4,12)$, matching the provided grid's plotted shape. The simplified equation $y=3|x|$ produces this symmetric absolute value graph.