Question

evaluate the piecewise function at the given values of the independent variable.
\\(g(x)=\

$$\begin{cases}x + 3&\\text{if }x\\geq - 3\\\\-(x + 3)&\\text{if }x < - 3\\end{cases}$$

\\)

a. \\(g(0)\\)
b. \\(g(-6)\\)
c. \\(g(-3)\\)

Explanation:

Step1: Evaluate g(0)

Check condition: $0 \geq -3$, use $g(x)=x+3$
$g(0)=0+3=3$

Step2: Evaluate g(-6)

Check condition: $-6 < -3$, use $g(x)=-(x+3)$
$g(-6)=-(-6+3)=-(-3)=3$

Step3: Evaluate g(-3)

Check condition: $-3 \geq -3$, use $g(x)=x+3$
$g(-3)=-3+3=0$

Answer:

a. $g(0)=3$
b. $g(-6)=3$
c. $g(-3)=0$