Piecewise function formula from graph | Functions and their graphs | Algebra II | Khan Academy

The video introduces piecewise functions, which are defined differently over various intervals. The example graph shows a function that is constant for different x-intervals, resembling a step function.

The first interval is from x > -9 to x <= -5. For this interval, the function f(x) is constant at -9. It's crucial to note the open circle at -9 (not including -9) and the closed circle at -5 (including -5).

The second interval is from x > -5 to x <= -1. In this range, the function f(x) is constant at 6. The video highlights that at x=-5, the function is defined by the first interval, preventing a single input from having multiple outputs.

The final interval is from x > -1 to x <= 9, where the function f(x) is constant at -7. This completes the piecewise definition of the function, demonstrating how this notation clarifies function behavior over different segments. The video concludes by emphasizing the enjoyment of working with piecewise functions.