Question

Determine the domain and range of the piece wise function. Then write an equation for the function. The domain of the function is [_,_].The range of the function is (_,_).What is the equation of the function?

Answer 1

Let:

$\begin{gathered} (x1,y1)=(-10,2) \\ (x2,y2)=(-2,10) \\ m=\frac{10-2}{-2-(-10)}=\frac{8}{8}=1 \end{gathered}$

so:

$\begin{gathered} y-y1=m(x-x1) \\ y-2=1(x-(-10)) \\ y-2=1(x+10) \\ y-2=x+10 \\ y=x+12 \end{gathered}$

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Let:

$\begin{gathered} (x1,y1)=(0,-6) \\ (x2,y2)=(5,4) \\ m=\frac{4-(-6)}{5-0}=\frac{10}{5} \\ m=2 \end{gathered}$

so:

$\begin{gathered} y-y1=m(x-x1) \\ y-(-6)=2(x-0) \\ y+6=2x \\ y=2x-6 \end{gathered}$

Therefore, the function is:

$f(x)=\begin{cases}x+12,_{\text{ }}if_{\text{ }}-10\le x<2 \\ 2,_{\text{ }}if_{\text{ }}-2\le x\le0 \\ 2x-6,_{\text{ }}if_{\text{ }}0The domain of the function is:

[tex]\begin{gathered} -10\le x\le5 \\ \lbrack-10,5\rbrack \end{gathered}$

The range of the function is:

[tex]\begin{gathered} -6