Question

given the function:
$f(x) = \

$$\begin{cases} 8x - 6 & x < 0 \\\\ 8x - 12 & x \\geq 0 \\end{cases}$$

$
calculate the following values:
$f(-1) = \square$
$f(0) = \square$
$f(2) = \square$

Explanation:

Step1: Calculate \( f(-1) \)

Since \(-1 < 0\), we use the first part of the piecewise function \( f(x) = 8x - 6 \).
Substitute \( x = -1 \) into \( 8x - 6 \):
\( f(-1) = 8(-1) - 6 = -8 - 6 = -14 \)

Step2: Calculate \( f(0) \)

Since \( 0 \geq 0 \), we use the second part of the piecewise function \( f(x) = 8x - 12 \).
Substitute \( x = 0 \) into \( 8x - 12 \):
\( f(0) = 8(0) - 12 = 0 - 12 = -12 \)

Step3: Calculate \( f(2) \)

Since \( 2 \geq 0 \), we use the second part of the piecewise function \( f(x) = 8x - 12 \).
Substitute \( x = 2 \) into \( 8x - 12 \):
\( f(2) = 8(2) - 12 = 16 - 12 = 4 \)

Answer:

\( f(-1) = -14 \)
\( f(0) = -12 \)
\( f(2) = 4 \)