Introduction to Functions

Functions are important in algebra and precalculus. They are operations that act upon a given input to change it into a single output. For instance, the function that adds three and then multiplies by 2 could be written as f(x) = 2(x+3). Functions cannot have more than one output per input. This means that a graph of a function must pass the so-called 5:36 vertical line test; a vertical line cannot intersect the graph of a function at more than one point. We conclude the video with an 6:22 example from physics of a functional relationship. It turns out that the speed of an object in a circular orbit about the earth is a function of the radius of the orbit. In other words, given an input of an orbital radius, there is only one possible output for the speed of the orbit at that radius. One cannot choose to orbit at a different speed at that radius.

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