Question

f(x) = \

$$\begin{cases}-x - 2&\\text{if }x < - 2\\\\\\frac{5}{2}x&\\text{if }x\\geq - 2\\end{cases}$$

select points on the graph to plot them. select \point fill\ to change a point from closed to open.

Explanation:

Step1: Consider \(x < - 2\) case

For \(y=-x - 2\), when \(x=-3\), \(y=-(-3)-2=1\).

Step2: Consider \(x\geq - 2\) case

For \(y = \frac{5}{2}x\), when \(x=-2\), \(y=\frac{5}{2}\times(-2)=-5\); when \(x = 0\), \(y=\frac{5}{2}\times0 = 0\); when \(x=2\), \(y=\frac{5}{2}\times2=5\).

Answer:

Points to plot: For \(y=-x - 2\) (\(x < - 2\)): \((-3,1)\) (open - circle as \(x < - 2\)). For \(y=\frac{5}{2}x\) (\(x\geq - 2\)): \((-2,-5)\) (closed - circle as \(x\geq - 2\)), \((0,0)\) (closed - circle), \((2,5)\) (closed - circle).