We consider applications of simple graphs to the analysis of measurable physical things that may vary with time. Each number t is regarded as the measure, in some convenient unit, of the time from some specified instant τ, after τ if t > 0, before τ if t < 0. Suppose G is a number set each element of which is so regarded. For each t in G, suppose f(t) is the measure (a number) of some physical thing at time t (i.e., at the time from τ determined by t). Then f is a simple graph whose X-projection is G.

Example. Suppose a spherical balloon is being inflated with a gas in such a way that the volume enclosed increases steadily, from a certain instant τ, at the rate of 200 cubic feet per minute. Each number t in the interval [0, a] represents the time measured in minutes from τ. Some simple graphs with X-projection [0, a] that arise are

1. i. the volume V such that if t is in [0, a], V (t) is the volume of gas enclosed by the balloon at time t so V(t) = 200t + V(0);

2. ii. the surface area s such that if t is in [0, a], s(t) is the area of the surface of the balloon; and

3. iii. the radius r such that if t is in [0, a], r(t) is the radius of the balloon.