Question

given the function:
$f(x) = \

$$\begin{cases} 5x - 3 & x < 0 \\\\ 5x - 6 & x \\geq 0 \\end{cases}$$

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

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

Since \( -1 < 0 \), we use the first part of the piecewise function \( f(x) = 5x - 3 \).
Substitute \( x = -1 \) into \( 5x - 3 \):
\( f(-1) = 5(-1) - 3 = -5 - 3 = -8 \)

Step2: Calculate \( f(0) \)

Since \( 0 \geq 0 \), we use the second part of the piecewise function \( f(x) = 5x - 6 \).
Substitute \( x = 0 \) into \( 5x - 6 \):
\( f(0) = 5(0) - 6 = 0 - 6 = -6 \)

Step3: Calculate \( f(2) \)

Since \( 2 \geq 0 \), we use the second part of the piecewise function \( f(x) = 5x - 6 \).
Substitute \( x = 2 \) into \( 5x - 6 \):
\( f(2) = 5(2) - 6 = 10 - 6 = 4 \)

Answer:

\( f(-1) = -8 \)
\( f(0) = -6 \)
\( f(2) = 4 \)