Question

a piecewise function is defined as shown.
$f(x) = \

$$\begin{cases} -x, & x \\leq -1 \\\\ 1, & x = 0 \\\\ x + 1, & x \\geq 1 \\end{cases}$$

$
what is the value of $f(x)$ when $x = 3$?
\\(\circ\\) $-3$
\\(\circ\\) $-2$
\\(\circ\\) $1$
\\(\circ\\) $4$

Explanation:

Step1: Determine the applicable piece of the function

Given \( x = 3 \), we check the conditions of the piecewise function. The conditions are \( x \leq -1 \), \( x = 0 \), and \( x \geq 1 \). Since \( 3 \geq 1 \), we use the piece \( f(x)=x + 1 \).

Step2: Substitute \( x = 3 \) into the chosen piece

Substitute \( x = 3 \) into \( f(x)=x + 1 \). So \( f(3)=3 + 1 \).

Step3: Calculate the result

\( 3+1 = 4 \).

Answer:

4