Question

1. $f(x)=\

$$\begin{cases}2x + 5 & \\text{if } x < -4 \\\\ x^2 + 3x & \\text{if } x \\geq -4\\end{cases}$$

$

Explanation:

Assuming we need to evaluate \( f(x) \) at a specific value (since the problem isn't fully stated, let's assume a common case, e.g., \( x = -5 \) and \( x = -4 \) to show how to use the piecewise function).

For \( x = -5 \):

Step1: Determine the piece.

Since \( -5 < -4 \), we use \( f(x) = 2x + 5 \).

Step2: Substitute \( x = -5 \).

\( f(-5) = 2(-5) + 5 \)

Step3: Calculate.

\( f(-5) = -10 + 5 = -5 \)

For \( x = -4 \):

Step1: Determine the piece.

Since \( -4 \geq -4 \), we use \( f(x) = x^2 + 3x \).

Step2: Substitute \( x = -4 \).

\( f(-4) = (-4)^2 + 3(-4) \)

Step3: Calculate.

\( f(-4) = 16 - 12 = 4 \)

If you meant to evaluate at a different \( x \), follow the same logic: check which inequality \( x \) satisfies, then substitute into the corresponding function.

For example, if \( x = 0 \) (which is \( \geq -4 \)):

Step1: Determine the piece.

\( 0 \geq -4 \), so use \( f(x) = x^2 + 3x \).

Step2: Substitute \( x = 0 \).

\( f(0) = 0^2 + 3(0) = 0 \)

Answer:

(for \( x = -5 \)): \(-5\)