End behavior of polynomials

Here is a PowerPoint I use when introducing end-behavior of polynomial functions. For each slide everyone raises arms or lowers arms to indicate the end-behavior of the polynomial. The left arm indicates what happens to \(y\) as \(x\rightarrow -\infty \) and the right arm indicates what happens to \(y\) as \(x\rightarrow \infty \).

So, for example, for \(f(x)=x^2\) you would put both arms up, while for \(f(x)=x^3\) you would put your left arm down and your right arm up. (I find it helpful to draw the four types of polynomial end behavior on the board at the front of the room, so that people can match their arms to a picture rather than having to think about left and right.)

This is a nice five- or ten-minute activity which gets people moving and developing understanding and helps you quickly get a sense of who is understanding and how well.