This light exercise is to get your students thinking about polynomial graph behavior. You could extend this exercise to guess they degrees and signs of the leading coefficients if desired. Simply print out a worksheet of all the letters of the alphabet and ask your students which letters are graphs of polynomials based on the following distinctions
- Polynomial graphs are continuous. You can draw them without lifting your pen
- Polynomial graphs have no sharp corners or cusps, they are smooth (see pic below).
See mathisfun.com for a great tutorial and pics.