Question

Graph each function.

$f\left(x\right)=\left\{\begin{array}{l}2x-1\text{if}x<2\\ x-3\text{if}x\ge 2\end{array}\right.$

Short answer

The required graph is represented by

Step-by-step solution

Step 1. Determine the points where the graph of the provided function is starting.

Substitute 0 in place of $x$into the provided function to get the required point for the first condition.

$$\begin{gathered} f\left(0\right)=2\cdot 0-1 \\ =-1 \end{gathered}$$

So the point is represented by $\left(0,-1\right)$.

Substitute 3 in place of $x$into the provided function to get the required point for the second condition.

$$\begin{gathered} f\left(3\right)=3-3 \\ =0 \end{gathered}$$

So the point is represented by $\left(3,0\right)$.

Step 2. Take the help of the obtained point. 

Take the help of obtained points and sketch the graphical representation of the provided function and the graph will consist of two figures as there are two different conditions.

Step 3. Write the conclusion. 

The obtained graph is completely defining the provided function so it is the required graph.