(NBI) A problem I’m looking forward to

One of the prompts for week 3 of the new blogger initiation is to show a math problem that we particularly like. In preparation for all of my new classes this summer, I spent quite a bit of time working through all the homework problems.  I came across one at the end of chapter 2 in my precalculus book that I am really excited for.  It is at the end of a unit on polynomial functions. A large portion of the unit is spent on characteristics of the graphs of polynomials and curve sketching.  Key things like the sign of the leading coefficient, degree of the polynomial, and symmetry based upon if the function is even or odd are what is focused on in the instruction.

Not the actual graph in the book, but a similar one found in google image search. The graph in the book shows reflection about the y-axis

List at least three reasons that the graph shown is not the graph off(x)={-4x^3-3x^2+5x+2}.

I really like this problem for a few reasons. I think it really does a good job synthesizing all of the material covered in the unit. A student who correctly answers shows that they understand the necessary concepts covered in the unit. It also gets students writing instead of just “solving math problems,” which is a point of emphasis of our administrator this year. I’m looking forward to see what my students do with this problem when the time comes. I’ll let you know when we get there!

What do you think?

Until next time . . .