Question

Express the function graphed on the axes below as a piecewise function.10864-10-8-6-42.46810

Answer 1

(1, -2)(0, -3)

Let's find the slope

$m=\frac{-3+2}{0-1}=\frac{-1}{-1}=1$

let's find the y-intercept

$\begin{gathered} y=mx+b \\ y=x+b \\ -3=b \\ b=-3 \end{gathered}$

Therefore,

$y=x-3$

Now to the second line by the right

(1, -4)(2, -5)

$m=\frac{-5+4}{2-1}=-1$$\begin{gathered} y=mx+b \\ y=-x+b \\ -4=-1+b \\ b=-3 \end{gathered}$

Therefore,

$y=-x-3$

The precise equation can be represented as follows

[tex]f(x)=\begin{cases}x-3\text{ for 1>}x\ge-6 \\ -x-3\text{ for 1}