Question

Express the function graphed on the axes below as a piecewise function.86-10-8-6-4-2810-4-6-8-10

Answer 1

Picking any two points on the line on the Right Hand side of the graph, we have the following coordinates:

`(6,0)\text{ and (8,3)}`

Finding the equation of the line with the coordinates above, we have::

`\begin{gathered} (y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \\ (3-0)/(8-6)=(y-0)/(x-6) \\ (3)/(2)=(y)/(x-6) \\ 2y=3(x-6) \\ 2y=3x-18 \\ y=(3x)/(2)-(18)/(2) \\ y=1.5x-9 \end{gathered}`

Picking any two points on the line on the left-hand side of the graph, we have the following coordinates:

`(-6,4)\text{ and (-4,3)}`

Finding the equation of the line with the coordinates above, we have::

`\begin{gathered} (y_2-y_1)/(x_2-x_1)=(y-y_1)/(x-x_1) \\ (3-0)/(8-6)=(y-0)/(x-6) \\ (3)/(2)=(y)/(x-6) \\ 2y=3(x-6) \\ 2y=3x-18 \\ y=(3x)/(2)-(18)/(2) \\ y=1.5x-9 \end{gathered}`

Hence, the piecewise function of the function; Y= 1.5x - 9 is