Question

Express the function graphed on the axes below as a piecewise function.104-10-8-6-4-2246810-6

Answer 1

Step 1

Find the equation of both lines using

`(y_2-y_1)/(x_2-x_1)=\text{ }(y-y_1)/(x-x_1)`

Where,

`\begin{gathered} y_1=-9 \\ y_2=\text{ -2} \\ x_1=\text{ -6} \\ x_2=1 \end{gathered}`

Hence,

`(-2-(-9))/(1-(-6))=(y-(-9))/(x-(-6))`
`\begin{gathered} (7)/(7)=(y+9)/(x+6) \\ y+9\text{ = x+6} \\ y\text{ = x+6-9} \\ y\text{ = x-}3 \end{gathered}`

For the second line we will have

`\begin{gathered} (-4-(-8))/(1-5)=\text{ }\frac{y-(-8)_{}}{x-5} \\ (4)/(-4)=(y+8)/(x-5) \\ -1(x-5)\text{ = y+8} \\ -x+5\text{ = y+8} \\ y\text{ =- x+5-8} \\ y\text{ = -x-3} \end{gathered}`

Step 2

Hence expressed the graphed solution as a piecewise function

[tex]f(x)=\begin{cases}x-3,-6\leq x<1 \\ \square \\ -x-3,-1