Question

evaluate the piecewise function at the given values of the independent variable.
$f(x)=\

$$\begin{cases}2x + 3&\\text{if }x < 0 \\\\ x + 5&\\text{if }x\\geq0 \\end{cases}$$

$
(a) $f(-2)$
(b) $f(0)$
(c) $f(4)$

Explanation:

Step1: Evaluate f(-2): pick x<0 rule

Since $-2 < 0$, use $f(x)=2x+3$.

$$\begin{align*} f(-2)&=2(-2)+3\\ &=-4+3 \end{align*}$$

Step2: Calculate f(-2) result

$$\begin{align*} f(-2)&=-1 \end{align*}$$

Step3: Evaluate f(0): pick x≥0 rule

Since $0 \geq 0$, use $f(x)=x+5$.

$$\begin{align*} f(0)&=0+5 \end{align*}$$

Step4: Calculate f(0) result

$$\begin{align*} f(0)&=5 \end{align*}$$

Step5: Evaluate f(4): pick x≥0 rule

Since $4 \geq 0$, use $f(x)=x+5$.

$$\begin{align*} f(4)&=4+5 \end{align*}$$

Step6: Calculate f(4) result

$$\begin{align*} f(4)&=9 \end{align*}$$

Answer:

(a) $f(-2) = -1$
(b) $f(0) = 5$
(c) $f(4) = 9$