91Ó°ÊÓ

A function that is written using two or more expression is called a piecewise function.

The given function is piecewise function as it consists different rays, segments and curves.

Consider the graph.

For $x<-1$the function is the constant function $f\left(x\right)=2$.

For $-1≤x≤1$ the function is a line with the slope of 2 and y-intercept 0, so $f\left(x\right)=2x$.

For $x>1$the function is a line with the slope of $-1$and passes through the point localid="1647304002114" $(2,-2)$.

Now use the point slope form to determine the equation of line.

localid="1647304063580" $\begin{array}{l}(y−y_1)=m(x−x_1)\\ (y−(-2\left)\right)=−1(x-2)\\ y=−x+2−2\\ y=−x\end{array}$.

Thus, $f\left(x\right)=-x$for $x>1$

Hence, the function is $f\left(x\right)=\{\begin{array}{l}2\text{ â¶Ä‰â¶Ä‰â¶Ä‰}if\text{ â¶Ä‰}x<−1\\ 2x\text{ â¶Ä‰â¶Ä‰â¶Ä‰}if\text{ â¶Ä‰}−1≤x≤1\\ −x\text{ â¶Ä‰â€‰}if\text{ }x>1\end{array}$.