1-C Continuity
Instructions
Use the slider tool on the left to change between three examples of graphs. Use the slider tool for c to move the point across the graph and observe the function values. On the third example, notice that a slider tool appears which you can use to manipulate the value of the function at x=3.
1-C Continuity
Describing the motion of moving objects is one of the major applications of Calculus. One important characteristic of motion in the real world is that teleportation is not possible (except maybe at the atomic level? I don't understand quantum mechanics). I can't move from one side of the room to the other without crossing every point "in between." This is essentially the motivation for the mathematical concept of continuity.
Continuity can be described (informally) in many different ways:
- The function values stay close together when the input values are close together (i.e., small changes in input lead to relatively small changes in output).
- The graph of the function is connected (at a point).
- The function cannot move from one output to another without taking on every possible output in between.