Question

y = -2|x| + 5
column by column
x |x| -2|x| y = -2|x| + 5
-3
-2
-1
0
1
2
3

Explanation:

Step1: Calculate \(|x|\) for \(x = -3\)

The absolute value of a number \(x\) is defined as \(|x|=

$$\begin{cases}x, & x\geq0\\ -x, & x < 0\end{cases}$$

\). For \(x=-3\) (which is less than 0), \(| - 3|=-(-3) = 3\).

Step2: Calculate \(-2|x|\) for \(x = -3\)

Substitute \(|x| = 3\) into \(-2|x|\). So, \(-2\times| - 3|=-2\times3=-6\).

Step3: Calculate \(y=-2|x| + 5\) for \(x = -3\)

Substitute \(-2|x|=-6\) into the equation \(y=-2|x| + 5\). Then \(y=-6 + 5=-1\).

Answer:

For \(x = - 3\), \(|x| = 3\), \(-2|x|=-6\), \(y=-1\) (filling the blue - colored cells with 3, - 6, - 1 respectively)