# Parametric Plots: A Creative Outlet - Parameterizing Function Graphs

Author(s):
Judy Holdener and Keith Howard

Parameterizing functions is easy. If y = f(x), then the parametric equations x(t) = t and
y(t) = f(t) always work. (That, is you simply treat x as the parameter). For example, if you want to parametrize the graph of the function f(x) = x3 + 2x2 - x + 9 from (0, 9) to (2, 23), then the parameterization is:

x(t) = t and y(t) = t3 + 2t2 - t + 9, 0 t 2.

Exercise 4.1

Figure 4.1 - The graph of a function

1. Find a parameterization of the function shown in Figure 4.1. [Hint: The right-most point on the graph is (5, 0).]

2. Now find a parameterization that traces out the same curve in the reverse direction.

3. Finally find a parameterization (x(t), y(t)) that satisfies x(0) = 0 and x(2) = 5.

Exercise 4.2

Figure 4.2 - A graph of a piecewise function

Find a parameterization of the piecewise-defined function shown in Figure 4.2. (Hint: This function can be plotted in two steps. Plot one piece on the MAPLET and then plot the other without clearing.)

Judy Holdener and Keith Howard, "Parametric Plots: A Creative Outlet - Parameterizing Function Graphs," Convergence (August 2004)

## JOMA

Journal of Online Mathematics and its Applications