Question

1. $f(x)=\

$$\begin{cases}x + 1 & \\text{if} & x < 0 \\\\ -x + 1 & \\text{if} & 0 \\leq x \\leq 2 \\\\ x - 1 & \\text{if} & x > 2\\end{cases}$$

$
evaluate:
a. $f(x)=0$ ______
b. $f(-4)=$ ______
grid graph

1. $f(x)=\begin{cases}3x - 14 & \text{if} & x \leq 4$

Explanation:

Part a: Solve f(x)=0

Step1: Check x<0 case

Set $x+1=0$ → $x=-1$ (valid, since -1<0)

Step2: Check 0≤x≤2 case

Set $-x+1=0$ → $x=1$ (valid, since 0≤1≤2)

Step3: Check x>2 case

Set $x-1=0$ → $x=1$ (invalid, since 1≤2)

Part b: Calculate f(-4)

Step1: Determine domain of -4

-4 < 0, use $f(x)=x+1$

Step2: Compute value

$f(-4)=-4+1=-3$

Answer:

a. x = -1, 1
b. -3