Teach 180: WODB (Day 73)

I love it when I reach into my folder from last year for a particular chapter and discover engaging activities that I had forgotten about. "Which One Doesn't Belong"? is a great way to open up discussion at the beginning of a class.  Or it can be used to help break up a long class.

This year, I used it as a class opener.  We had just finished a unit on polynomial functions.  Each table of students was asked to identify which one they thought didn't belong.  Usually students don't pick up on the line-type (dotted vs solid) or the color of the graph, but these students did.  So next, I asked for a mathematical reason for why a function wouldn't belong.

Here are some answers my students gave me.

Top Left: Has same end behavior on both left and right.  Others rise on one side and fall on the other for end behavior.
Top Right: It is the only function where the graph crosses at x = 0, instead of touching and turning.
Bottom Right: It is the only graph that is not in the fourth quadrant.

The bottom left was the most challenging.  What about the graph makes it different than the others?  One of my students said it was the only one to have a minimum in the 4th quadrant, but that wasn't true.  Someone else suggested that it was the only one to have a x-intercept of 3.  But that wasn't true, either.

We finally decided on the following.  The bottom left function doesn't belong, because is the only one that has both positive and negative y-values when x is positive.  Can you find any other reasons why the bottom left function doesn't belong?