Question

first score: first attempt due: final corrections due: final score: 2 evaluate: f(-4) = f(-3) = f(-1) = f(3) = zeros: y-intercept: domain: range: extrema: inc/dec/constant: continuity: end behavior: equation: f(x) = { x, ________ √x, ________

Explanation:

Step1: Find f(-4)

Check x=-4 on the line segment: f(-4)=-2

Step2: Find f(-3)

Check x=-3 on the line segment: f(-3)=0

Step3: Find f(-1)

Check x=-1 on the curve: f(-1)=-1

Step4: Find f(3)

Check x=3 on the curve: f(3)=-4

Step5: Identify zeros

x where f(x)=0: x=-3

Step6: Find y-intercept

x=0: f(0)=-1

Step7: Determine domain

All x from -4 to 4: [-4,4]

Step8: Determine range

All y from -4 to 2: [-4,2]

Step9: Check extrema

Maximum at x=-1.5: 2; Minimum at x=4: -4

Step10: Check inc/dec intervals

Increasing: [-4,-1.5]; Decreasing: [-1.5,4]

Step11: Check continuity

Continuous at all domain points

Step12: Analyze end behavior

As x→-4+, f(x)→-2; As x→4-, f(x)→-4

Step13: Write piecewise equation

Line: y=2x+6 (-4≤x≤-1); Curve: y=-√(-x) (-1≤x≤4)

Answer:

f(-4)=-2
f(-3)=0
f(-1)=-1
f(3)=-4
Zeros: x=-3
y-intercept: -1
Domain: [-4,4]
Range: [-4,2]
Extrema: Max=2 at x=-1.5, Min=-4 at x=4
Inc/Dec/Constant: Increasing on [-4,-1.5], Decreasing on [-1.5,4]
Continuity: Continuous on [-4,4]
End Behavior: As x→-4+, f(x)→-2; As x→4-, f(x)→-4
Equation: \( f(x)=

$$\begin{cases}2x+6, & -4\leq x\leq -1 \\ -\sqrt{-x}, & -1\leq x\leq 4\end{cases}$$

\)