Question

Express the function graphed on the axes below as a piecewise function.1086.6810-10-8-6-4-2-2-6-8-10

Answer 1

To determine the graphed on the axes below as a piecewise function

$\text{ For line 1 y =3}$$\begin{gathered} \text{For line 2 } \\ x_1\text{ = }0 \\ y_1\text{ = 1} \\ x_2\text{ = }5 \\ y_2\text{ = -4} \end{gathered}$

The equation of line using two-point form will be

$\begin{gathered} y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1) \\ y-1=\frac{-4-1}{5-0}(x-0) \\ y-1=\frac{-5}{5}(x)_{} \\ y-1=-1(x) \\ y=-x+1 \end{gathered}$

Thus for each of the line the range of values are

[tex]\begin{gathered} y=3\Rightarrow\mleft\lbrace-5\leq x<0\mright\rbrace \\ y=-x+1\Rightarrow\mleft\lbrace0Therefore the piecewise function for the lines will be[tex]f(x)=\begin{cases}y=3,\mleft\lbrace-5\leq x<0\mright\rbrace \\ \\ y=-x+1,\text{ }\mleft\lbrace0