Question

lesson 1.2 homework
complete problems 3, 4, 6, 8, 9, 11, 13, 15, 18, 21, 31, and 35 for independent practice.
when you are finished, check the solutions with your teacher.
evaluate the function. (see example 1)
$f(x)=\

$$\begin{cases} 5x - 1, & \\text{if } x < -2 \\\\ x + 3, & \\text{if } x \\geq -2 \\end{cases}$$

$

1. $f(-3)$

$x = -3$
$f(x) = 5x - 1$
$f(-3) = 5 \times (-3) - 1$
$5 \times (-3) = -15$
$-15 - 1 = -16$

1. $f(-2)$

$x = -2$
$f(x) = x + 3$
$f(-2) = -2 + 3$
$-2 + 3 = 1$

1. $f(5)$

$x = 5$
$x = 5$ into $f(x) = x + 3$
$f(5) = 5 + 3$
$5 + 3 = 8$

Explanation:

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

Step1: Determine the function rule

The function is piecewise: \( f(x) =

$$\begin{cases} 5x - 1, & \text{if } x < -2 \\ x + 3, & \text{if } x \geq -2 \end{cases}$$

\). For \( x = -3 \), since \( -3 < -2 \), we use \( f(x) = 5x - 1 \).

Step2: Substitute \( x = -3 \) into \( 5x - 1 \)

\( f(-3) = 5(-3) - 1 \)

Step3: Calculate the value

\( 5(-3) = -15 \), so \( -15 - 1 = -16 \).

Step1: Determine the function rule

For \( x = -2 \), since \( -2 \geq -2 \), we use \( f(x) = x + 3 \).

Step2: Substitute \( x = -2 \) into \( x + 3 \)

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

Step3: Calculate the value

\( -2 + 3 = 1 \).

Step1: Determine the function rule

For \( x = 5 \), since \( 5 \geq -2 \), we use \( f(x) = x + 3 \).

Step2: Substitute \( x = 5 \) into \( x + 3 \)

\( f(5) = 5 + 3 \)

Step3: Calculate the value

\( 5 + 3 = 8 \).

Answer:

\( f(-3) = -16 \)

Problem 4: Evaluate \( f(-2) \)