Polynomial Symmetry vs. Polynomial End Behavior

Let me dramatically reenact any given pre-calculus, algebra, or calculus class to you from my past almost decade of teaching....

Scenario #1:

Student: "This function is even."

Me: (Secretly lighting up inside because they understood the lesson!) "Why do you say that?"

Student: "Because both ends go up!"

**Face Palm**

Scenario #2: 

Student: "The function has an odd degree."

Me: (Secretly lighting up inside because they understood the lesson!) "Why do you say that?"

Student: "Because it's symmetric about the origin!"

**Face Palm"

Does this sound familiar to anyone else? 

I am fighting the good fight this year and preemptively planning an activity for my A2 students to work on to get them thinking about the differences between symmetry and end behavior. 

Symmetry vs. End Behavior Activity

It starts with students identifying both the symmetry and degree of given polynomials:

Then, asks them to agree or disagree with some statements about symmetry and degree:

Then, finally, asks them to draw their own pictures to fit constraints. 

Will report back on how this goes. If you have any tricks to help students keep these straight, please share!