Question

swer attempt 1 out of 2
$f(x) = \

$$\begin{cases} \\boxed{-4} & \\text{for } \\boxed{-3 \\leq x \\leq 2} \\\\ \\boxed{3x\\ \\text{i}} & \\text{for } \\boxed{2 < x \\leq 5} \\end{cases}$$

$

Explanation:

Step1: Identify linear segment equation

We use two points on the line: $(5,1)$ and $(2,-8)$. First calculate slope:
$m=\frac{1-(-8)}{5-2}=\frac{9}{3}=3$
Then use point-slope form $y-y_1=m(x-x_1)$ with $(5,1)$:
$y-1=3(x-5)$
Simplify: $y=3x-15+1=3x-14$

Step2: Verify the equation

Check $x=2$: $y=3(2)-14=6-14=-8$, which matches the open point. Check $x=5$: $y=3(5)-14=15-14=1$, which matches the closed point.

Answer:

The correct expression for the interval $2 < x \leq 5$ is $\boldsymbol{3x - 14}$, so the piecewise function is:

$$ f(x) =
LATEXBLOCK0
$$