Question

express the function graphed on the axes below as a piecewise function.
answer attempt 1 out of 2
$f(x) = \

$$\begin{cases} \\boxed{} \\text{for } \\boxed{} \\\\ \\boxed{} \\text{for } \\boxed{} \\end{cases}$$

$

Explanation:

Step1: Identify left segment points

Points: $(-6, -2)$ (closed), $(-2, 4)$ (open)

Step2: Find left segment slope

Slope $m=\frac{4-(-2)}{-2-(-6)}=\frac{6}{4}=\frac{3}{2}$

Step3: Left segment equation

Use point-slope: $y-(-2)=\frac{3}{2}(x-(-6))$
Simplify: $y+2=\frac{3}{2}x+9 \implies y=\frac{3}{2}x+7$
Domain: $-6 \leq x < -2$

Step4: Identify right segment points

Points: $(-2, 4)$ (open), $(2, -2)$ (open)

Step5: Find right segment slope

Slope $m=\frac{-2-4}{2-(-2)}=\frac{-6}{4}=-\frac{3}{2}$

Step6: Right segment equation

Use point-slope: $y-4=-\frac{3}{2}(x-(-2))$
Simplify: $y-4=-\frac{3}{2}x-3 \implies y=-\frac{3}{2}x+1$
Domain: $-2 < x < 2$

Answer:

$$ f(x) =
LATEXBLOCK0
$$