function, linear function, nonlinear function
TEKS 8(1)(E), 8(1)(G), 8(5)(C), 8(5)(G)
Think of a juggler's ball being tossed in the air and falling back down. The relationship between speed and time is not always the same:
• As the ball rises, the speed decreases.
• As the ball falls, the speed increases.
The table shows the height of a juggling ball at a given time. You can plot the data from the table on a graph.
Rate of change is the change in the outputs divided by the change in the inputs. The rate of change is not constant. In cases like these, nonlinear functions are needed to describe how the variables are related. Nonlinear functions are functions that do not have a constant rate of change. The graph of a nonlinear function is not a straight line.