Question

1. $y = \frac{1}{2}|x|$
2. $y = $

Explanation:

Step1: Define absolute value cases

The absolute value function splits into two linear cases:
For $x \geq 0$, $y = \frac{1}{2}x$; for $x < 0$, $y = \frac{1}{2}(-x) = -\frac{1}{2}x$

Step2: Plot key points (non-negative x)

Choose $x=0$: $y=\frac{1}{2}(0)=0$ → point $(0,0)$
Choose $x=2$: $y=\frac{1}{2}(2)=1$ → point $(2,1)$
Choose $x=4$: $y=\frac{1}{2}(4)=2$ → point $(4,2)$

Step3: Plot key points (negative x)

Choose $x=-2$: $y=-\frac{1}{2}(-2)=1$ → point $(-2,1)$
Choose $x=-4$: $y=-\frac{1}{2}(-4)=2$ → point $(-4,2)$

Step4: Connect points to form graph

Draw a line from the left quadrant (using negative x points) through $(0,0)$ to the right quadrant (using non-negative x points), forming a V-shape.

Answer:

The graph is a V-shaped curve with vertex at $(0,0)$, passing through $(-4,2)$, $(-2,1)$, $(2,1)$, $(4,2)$, and following $y=\frac{1}{2}x$ for $x\geq0$ and $y=-\frac{1}{2}x$ for $x<0$.