Question

Graph each equation or inequality

$h\left(x\right)=\left\{\begin{array}{c}x+2\text{if}x<-2\\ 2x-1\text{if}x\ge -2\end{array}\right.$

Short answer

The graph of the equation$h\left(x\right)=\left\{\begin{array}{c}x+2\text{if}x<-2\\ 2x-1\text{if}x\ge -2\end{array}\right.$ is

Step-by-step solution

Step-1 – Apply the concept of Piece wise function

The piece wise function is a function which is defined using two or more expressions.

For example, $f\left(x\right)=\left\{\begin{array}{c}2x+1\text{if}x\le 5\\ x+2\text{if}x>5\end{array}\right.$. Here the function $f\left(x\right)$is defined by using two expressions.

Step-2 – Make a Table of values 

Make a table of values such that the values satisfy the equation

$h\left(x\right)=\left\{\begin{array}{c}x+2\text{if}x<-2\\ 2x-1\text{if}x\ge -2\end{array}\right.$.

Choose a value of x and find the corresponding value of $h\left(x\right)$.

Step-3 – Graph the tabled values

By using the values in the table, graph the equation.