Question

Express the fuction graphed on the axes below as a piecewise function

Answer 1

Concept

Find the equation of line for the second line.

x1 = -2 y1 = 1

x2 = -4 y2 = 2

Next, apply equation of a line formula

`\begin{gathered} \frac{y-y_1}{x-x_1\text{ }}\text{ = }(y_2-y_1)/(x_2-x_1) \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }\frac{2\text{ - 1}}{-4\text{ + 2}} \\ \frac{y\text{ - 1}}{x\text{ + 2}}\text{ = }(1)/(-2) \\ -2(y\text{ - 1) = 1(x + 2)} \\ -2y\text{ + 2 = x + 2} \\ -2y\text{ = x} \\ y\text{ = }(-1)/(2)x \end{gathered}`

Final answer

The graphed as a piecewise function ​is given below