Question

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

$$\begin{cases} 3x + 5 & \\text{if } x < 0 \\\\ 3x + 7 & \\text{if } x \\geq 0 \\end{cases}$$

$
(a) $f(-3)$
(b) $f(0)$
(c) $f(2)$

(a) $f(-3)=\square$
(b) $f(0)=\square$
(c) $f(2)=\square$

Explanation:

Step1: Evaluate \( f(-3) \)

Since \( -3 < 0 \), use \( f(x) = 3x + 5 \). Substitute \( x = -3 \):
\( f(-3) = 3(-3) + 5 = -9 + 5 = -4 \)

Step2: Evaluate \( f(0) \)

Since \( 0 \geq 0 \), use \( f(x) = 3x + 7 \). Substitute \( x = 0 \):
\( f(0) = 3(0) + 7 = 0 + 7 = 7 \)

Step3: Evaluate \( f(2) \)

Since \( 2 \geq 0 \), use \( f(x) = 3x + 7 \). Substitute \( x = 2 \):
\( f(2) = 3(2) + 7 = 6 + 7 = 13 \)

Answer:

(a) \( f(-3) = \boldsymbol{-4} \)
(b) \( f(0) = \boldsymbol{7} \)
(c) \( f(2) = \boldsymbol{13} \)