Which is the graph of the step function \( f(x) \) ? \( f(x)=\left\{\begin{array}{cc}-1, & x<-1 \\ 0, & -1 \leq x \leq 1 \\ 1, & x>1\end{array}\right. \)

To visualize the step function \( f(x) \), imagine a staircase. At \( x < -1 \), the function holds steady at -1, giving you a flat line that stretches leftward. As soon as you reach \( x = -1 \), it jumps up to 0, creating a vertical step. This flat line at 0 continues until you hit \( x = 1 \), where there's another upward jump to 1. Finally, after \( x = 1 \), the line remains constant at 1. The resulting graph is characterized by two jumps and three distinct intervals, reflecting the function's piecewise nature! The step function is often used in computer science and engineering. For example, it can represent a system's switching on and off – when a certain condition is met, the value jumps. Additionally, it helps in defining piecewise continuous functions, which are essential when dealing with real-world scenarios involving thresholds, such as in pricing models, signal processing, or control systems. This makes it a handy tool for anyone tackling problems that require a little ‘jump’ in their models!