Determining polynomial functions by Learning and Knowledge
Determining functions usually works like this:
1. You have a word problem that lists properties of the function, also called conditions. You need to identify these conditions and transform them into equations. This usually results in several equations, a system of linear equations. You have to solve this system, either by hand using Gaussian elimination or with a calculator, to find the function coefficients—the numbers that appear in front of the x-values. Sometimes, you only have the graph of a function, and you need to identify its properties. I'll cover this in the second third of the video. At the end, I'll work through a typical problem on this topic completely.
Please note, this video focuses exclusively on determining polynomial functions. While the basic procedure is the same for other functions, such as exponential or trigonometric functions, you won't end up with a system of linear equations that you can solve so easily using Gaussian elimination.