Domain & Range from a Graph

My students have never had such accuracy in identifying domain and range from a graph.

Thanks to this little unsuspecting guy.

I blindfolded him and gave him eyes on the sides of his head.

And then he took a stroll across the x-axis to find to find domain.

Now the x-values that are included in the domain can be determined by stating the x-values where our little friend can "see" the graph.

Can he see it here? No.

What about here? No.

What is the smallest x-value where he can see the graph?  -9

Can he see it here? Yes

What is the largest x-value where he can see the graph? 9

So the domain is [-9, 9]

To find range, he strolls up the y-axis.

For a function that doesn't have endpoints, we talked about what the function looks like beyond the plane that is shown. Students really didn't have trouble with this.

All this silliness is the result of desperation.

For the first time ever, I am teaching two levels of Algebra 2. I am finding that some of my "standard" explanations aren't working with the "not advanced" group.

So then I'm all "Okay, that didn't work. Here, let me grab this toy bug from my closet." And stuff like this happens.

What if My Students Use Programming to CHEAT?

One question comes up as I've recently dipped my toes into programming on calculators with my students . . . You teach your students to program, but what if they start programming formulas into their calculators?

I've been thinking about this question, and playing out a few scenarios in my head . . .

1. Don't teach students to program. Maintaining ignorance is a good way to keep students from doing things you don't want them to do.

2. Teach them to program, but make sure they don't use it for cheating. Reset calculators before every test. This is a good way to make sure students don't spend too much time on any programs.

3. Let them program away. What might happen? Student who learns about the quadratic formula might think about programming it into her calculator. Later on, student encounters an equation, recognizes it is quadratic, correctly identifies a, b, and c and then executes a program she has coded herself to solve the quadratic.

I think I can live with option 3.

In fact, I'm over here smiling.