Other than being the most feared f-word in math teaching, a “function” is a question with only one answer.

Take the question: “How tall are you?”

We can change this to: “What’s the height of you?”

And if we wanted to compare your height to other people’s heights we can ask: “What’s the height of <insert person’s name here>?” This is the question template – the formula.

You can answer this question in inches, feet or cm, but the *value* of the answer remains unique, based on the person.

And that last little piece of the sentence is what makes the difference, *based on the person.*

The question changes with this little change. *<cue music>* This is the **variable** in the equation.

And we say, “Height is a function of the person.”

### So where’s the fear come in?

As always, the notation is the kicker when it comes to teaching math.

Let’s change the question a little.

What’s the height of Enrique tomorrow if he grows three inches tonight?

Rather contrived, but work with me…

The question template is

What’s the height of <insert person’s name here> if he/she grows three inches tonight?

Which becomes

<height> = <height now> + 3

Or

*H = N + 3*

Egad!

And we haven’t even started with the *f(x)* stuff!

### What’s this “domain” thing about?

I wrote the first sentence of this post a little too hastily. A function has only one answer *if there’**s a valid question.*

If you ask, “How tall is love?” someone will laugh at you. Or think you’re from California.

Our question template included some specifics that you don’t normally get:

What’s the height of <insert person’s name here>?

If we instead ask, “What’s the height of *x*?” we would then have to ask: what kinds of things can we put in for *x*? Can we put concepts, like love? Or just objects? The kinds of things that you can put in for x is called the domain.

For our question, we would need to specify that *x* is a person.

What do you think? How does this feel when explaining it to your kids?

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