Q15. - Algebra 2

Question

Graph each equation or inequality

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

Step-by-Step Solution

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-1 &ndash; 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 &ndash; 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 &ndash; Graph the tabled values

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