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::

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

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::

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

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