Question

write the absolute value functions as a price wise function

Answer 1

`f(x) =\begin{cases}-2x -8&\text{if} \ x\geq-4\\ 2x+8&\text{if} \ x\leq-4\end{cases}`

Explanation:

solving the equation:

x + 4 = 0

x + 4 = 0

⇔ x + 4 - 4 = 0 - 4

⇔ x = - 4

Then

`\left\vert x+4\right\vert =\begin{cases}x+4&\text{if} \ x\geq-4\\ -x-4&\text{if} \ x\leq-4\end{cases}`

Then

`f(x) =\begin{cases}-2(x+4)&\text{if} \ x\geq-4\\ -2(-x-4)&\text{if} \ x\leq-4\end{cases}`

Then

`f(x) =\begin{cases}-2x -8&\text{if} \ x\geq-4\\ 2x+8&\text{if} \ x\leq-4\end{cases}`