Question

in the piecewise function below, what does y equal when x = -2? note: pay close attention to the < and ≥ signs. (chapter 2)
$y = \

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

$
\bigcirc 0
\bigcirc -5
\bigcirc y does not exist when x = -2
\bigcirc 3

Explanation:

Step1: Determine the applicable function

Given \( x = -2 \), we check the conditions. The second part of the piecewise function is for \( x \geq -2 \), so we use \( y = 2x - 1 \).

Step2: Substitute \( x = -2 \) into the function

Substitute \( x = -2 \) into \( y = 2x - 1 \): \( y = 2(-2) - 1 \).
Calculate: \( 2(-2) = -4 \), then \( -4 - 1 = -5 \)? Wait, no, wait: Wait, \( 2(-2) = -4 \), \( -4 - 1 = -5 \)? But wait, no, wait the options: Wait, no, wait I made a mistake. Wait, \( 2x - 1 \) when \( x = -2 \): \( 2(-2) - 1 = -4 - 1 = -5 \)? But the options have 0, -5, etc. Wait, no, wait maybe I messed up. Wait, no, let's re - calculate. Wait, \( 2(-2)=-4 \), \( -4 - 1=-5 \). But wait, the first option is 0, second is -5, third is y does not exist, fourth is 3. Wait, but wait, maybe I used the wrong function? Wait, the condition is \( x\geq - 2 \), so \( x = -2 \) satisfies \( x\geq - 2 \), so we use \( 2x - 1 \). So \( y = 2(-2)-1=-4 - 1=-5 \). But wait, the option -5 is there. But wait, wait, maybe I made a mistake. Wait, no, let's check again. Wait, \( 2x-1 \) at \( x = -2 \): \( 2(-2)=-4 \), \( -4 - 1=-5 \). So the answer should be -5? But wait, the option -5 is present. Wait, but the first option is 0, how? Wait, no, maybe I misread the function. Wait, the function is \( y=

$$\begin{cases}x + 5&x\lt - 2\\2x-1&x\geq - 2\end{cases}$$

\). So for \( x=-2 \), we use \( 2x - 1 \). So \( 2*(-2)-1=-5 \). So the answer is -5.

Answer:

-5