Question

1. $f(x) = \

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

$

Explanation:

Assuming the problem is to evaluate \( f(x) \) at a certain value (e.g., \( x = -5 \), \( x = -4 \), \( x = 0 \)), here's how to do it:

For \( x = -5 \) (since \( -5 < -4 \)):

Step 1: Identify the correct piece

Use \( f(x) = 2x + 5 \) because \( x = -5 < -4 \).

Step 2: Substitute \( x = -5 \)

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

Step 3: Simplify

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

For \( x = -4 \) (since \( -4 \geq -4 \)):

Step 1: Identify the correct piece

Use \( f(x) = x^2 + 3x \) because \( x = -4 \geq -4 \).

Step 2: Substitute \( x = -4 \)

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

Step 3: Simplify

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

For \( x = 0 \) (since \( 0 \geq -4 \)):

Step 1: Identify the correct piece

Use \( f(x) = x^2 + 3x \) because \( x = 0 \geq -4 \).

Step 2: Substitute \( x = 0 \)

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

Step 3: Simplify

\( f(0) = 0 + 0 = 0 \)

If you intended to evaluate at a different \( x \)-value, follow the same logic: check if \( x < -4 \) (use \( 2x + 5 \)) or \( x \geq -4 \) (use \( x^2 + 3x \)), then substitute and simplify.

For example, if the question was to find \( f(-5) \):

Answer:

\( \boldsymbol{-5} \)

If the question was to find \( f(-4) \):