When graphing a piecewise function, each piece must be considered separately. First, a piece is graphed for the values of its domain. Then an end or ends of the piece are marked with
These points are then marked and, as it is a linear function, joined with a straight line across the corresponding domain. The rule states that this piece is defined at x=-1. Therefore, the end is marked with a closed circle.
Removing all unnecessary information, the final graph of f is shown.
When determining points on a piecewise function, it is important to make sure that the correct piece of the function is used.To evaluate f(-1) we must use the first piece of the function, 2x+1, because x=-1 is an element of that domain. Therefore, we find that
When graphing step functions, as when graphing any piecewise function, each piece must be considered separately. Graph each piece across its domain. Mark the end or ends of with
To park a car at the Sombra Brothers Amusement Park costs $5 for the first two hours, then another $1.50 for each additional hour. Graph a function which describes the parking fee.
|total cost||number of hours parked|
Since the parking fee is constant across each interval this is a step function. We can graph each piece of the function separately by drawing a horizontal line at the total cost for the corresponding number of hours.
The lower end of each piece is marked with a closed circle, while the upper end is marked with an open circle.