Question

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

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

$

Explanation:

Step1: Identify left segment points

Points: $(-6, -4)$ (closed), $(0, 4)$ (open)

Step2: Find left segment slope

Slope $m_1 = \frac{4 - (-4)}{0 - (-6)} = \frac{8}{6} = \frac{4}{3}$

Step3: Left segment equation

Use point $(-6, -4)$: $y - (-4) = \frac{4}{3}(x + 6)$
Simplify: $y + 4 = \frac{4}{3}x + 8$ → $y = \frac{4}{3}x + 4$
Domain: $-6 \leq x < 0$

Step4: Identify right segment points

Points: $(0, 4)$ (open), $(2, 0)$ (open)

Step5: Find right segment slope

Slope $m_2 = \frac{0 - 4}{2 - 0} = \frac{-4}{2} = -2$

Step6: Right segment equation

Use point $(2, 0)$: $y - 0 = -2(x - 2)$
Simplify: $y = -2x + 4$
Domain: $0 < x < 2$

Answer:

$$ f(x) =
LATEXBLOCK0
$$