Question

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

$$\begin{cases} 5x + 4 & \\text{if } x < 0 \\\\ x + 7 & \\text{if } x \\geq 0 \\end{cases}$$

$
(a) $f(-2)$
(b) $f(0)$
(c) $f(1)$

Explanation:

Step1: Evaluate f(-2) (x<0 case)

Since $-2 < 0$, use $f(x)=5x+4$.
$f(-2)=5(-2)+4$
$f(-2)=-10+4=-6$

Step2: Evaluate f(0) (x≥0 case)

Since $0 \geq 0$, use $f(x)=x+7$.
$f(0)=0+7=7$

Step3: Evaluate f(1) (x≥0 case)

Since $1 \geq 0$, use $f(x)=x+7$.
$f(1)=1+7=8$

Answer:

(a) $f(-2) = -6$
(b) $f(0) = 7$
(c) $f(1) = 8$