How to Graph the Piecewise Constant Function $f(x)=\begin{cases} 2, x \leq -3 \\ -1, -3

Question

Graph the piecewise constant function $f(x)=\begin{cases} 2, & \text{if } x \leq -3 \\ -1, & \text{if } -3 < x < 3 \\ 3, & \text{if } x \geq 3 \end{cases}$

Accepted Answer

A piecewise graph with three horizontal segments: 1) A horizontal ray at $y=2$, including the point (-3,2) and extending left; 2) A horizontal line segment at $y=-1$, from open point (-3,-1) to open point (3,-1); 3) A horizontal ray at $y=3$, including the point (3,3) and extending right.

Answer

Step 1: Analyze the first piece $y = 2$ for $x \leq -3$. This is a horizontal line. Plot the closed dot at (-3,2) and draw a horizontal line extending to the left. Step 2: Analyze the second piece $y = -1$ for $-3 < x < 3$. This is a horizontal line segment. Plot open dots at (-3,-1) and (3,-1), then draw a horizontal line connecting the two open dots. Step 3: Analyze the third piece $y = 3$ for $x \geq 3$. This is a horizontal ray. Plot the closed dot at (3,3) and draw a horizontal line extending to the right. Step 4: Combine all three horizontal segments on the same coordinate plane to form the complete graph.