Question

determine the values below given the following piecewise function.
$f(x) = \

$$\begin{cases} x + 6 & \\text{if } x < 0 \\\\ 4x - 1 & \\text{if } x \\geq 0 \\end{cases}$$

$
find $f(-4)$.
$f(-4) = $

find $f(0)$.
$f(0) = $

find $f(3)$.
$f(3) = $

Explanation:

Step1: Determine the piece for \( f(-4) \)

Since \( -4 < 0 \), use \( f(x)=x + 6 \). Substitute \( x=-4 \):
\( f(-4)=-4 + 6 \)

Step2: Calculate \( f(-4) \)

\( -4 + 6 = 2 \)

Step3: Determine the piece for \( f(0) \)

Since \( 0 \geq 0 \), use \( f(x)=4x - 1 \). Substitute \( x = 0 \):
\( f(0)=4(0)-1 \)

Step4: Calculate \( f(0) \)

\( 4(0)-1 = -1 \)

Step5: Determine the piece for \( f(3) \)

Since \( 3 \geq 0 \), use \( f(x)=4x - 1 \). Substitute \( x = 3 \):
\( f(3)=4(3)-1 \)

Step6: Calculate \( f(3) \)

\( 4(3)-1 = 12 - 1 = 11 \)

Answer:

\( f(-4) = 2 \)
\( f(0) = -1 \)
\( f(3) = 11 \)