Question

the piecewise function (problems 5–7)
$f(x)=\

$$\begin{cases}3x, & x < 0 \\\\ x - 2, & 0 \\leq x \\leq 4 \\\\ x^2 - 4, & x > 4\\end{cases}$$

$
problems (evaluate)

1. $f(-1) = $
2. $f(3) = $
3. $f(5) = $

Explanation:

Problem 5: Evaluate \( f(-1) \)

Step 1: Determine the applicable piece

Since \( -1 < 0 \), we use the first piece of the piecewise function, which is \( f(x) = 3x \).

Step 2: Substitute \( x = -1 \) into the function

Substitute \( x = -1 \) into \( f(x) = 3x \):
\( f(-1) = 3(-1) \)
\( f(-1) = -3 \)

Step 1: Determine the applicable piece

Since \( 0 \leq 3 \leq 4 \), we use the second piece of the piecewise function, which is \( f(x) = x - 2 \).

Step 2: Substitute \( x = 3 \) into the function

Substitute \( x = 3 \) into \( f(x) = x - 2 \):
\( f(3) = 3 - 2 \)
\( f(3) = 1 \)

Step 1: Determine the applicable piece

Since \( 5 > 4 \), we use the third piece of the piecewise function, which is \( f(x) = x^2 - 4 \).

Step 2: Substitute \( x = 5 \) into the function

Substitute \( x = 5 \) into \( f(x) = x^2 - 4 \):
\( f(5) = 5^2 - 4 \)
\( f(5) = 25 - 4 \)
\( f(5) = 21 \)

Answer:

\( f(-1) = -3 \)

Problem 6: Evaluate \( f(3) \)