To graph the step function [tex]\( f(x) = \left\{
\begin{array}{cl}
-2 & ; x < -3 \\
1 & ; -3 \leq x < 2 \\
3 & ; x \geq 2 \\
\end{array}
\right. \)[/tex], follow these steps:
1. For [tex]\( x < -3 \)[/tex]:
- The function is constant and equal to [tex]\(-2\)[/tex].
- Use a solid point at [tex]\(( -3, -2 )\)[/tex] and draw a horizontal line extending to the left.
2. For [tex]\(-3 \leq x < 2\)[/tex]:
- The function is constant and equal to [tex]\(1\)[/tex].
- Use a solid point at [tex]\((-3, 1)\)[/tex] and draw a horizontal line extending to the right until [tex]\( x = 2 \)[/tex].
- Use an open point at [tex]\((2, 1)\)[/tex] because the interval does not include 2.
3. For [tex]\( x \geq 2 \)[/tex]:
- The function is constant and equal to [tex]\(3\)[/tex].
- Use a solid point at [tex]\((2, 3)\)[/tex] and draw a horizontal line extending to the right.
Here is a step-by-step guide to applying the drawing tools on the provided graph:
1. Select the Point tool:
- Place a solid point at [tex]\( (-3, -2) \)[/tex].
- Place a solid point at [tex]\( (-3, 1) \)[/tex].
- Place an open point at [tex]\( (2, 1) \)[/tex].
- Place a solid point at [tex]\( (2, 3) \)[/tex].
2. Select the Line Segment tool:
- Draw a horizontal line starting from [tex]\( (-3, -2) \)[/tex] extending to the left.
- Draw a horizontal line starting from [tex]\( (-3, 1) \)[/tex] extending to [tex]\( 2 \)[/tex].
- Draw a horizontal line starting from [tex]\( (2, 3) \)[/tex] extending to the right.
This will result in the correct graph depicting the described step function.
