Chapter 11
Functions
Feed a vending machine the same code twice and the same snack drops out both times. A parking meter works the same way: put in an amount of money, get back an amount of time. Algebra so far has asked which number makes a statement true, one answer at a time. What it has never done is give a name to the rule behind all those answers. Functions are that name. And once the rule has a name of its own, a new question arrives: what can you do to a rule itself?
What You'll Explore
4 lessons.
Some lessons are marked Advanced because they go beyond core Algebra I. Skip them or explore them if you are curious.
- What Is a Function?
Every rule you meet takes something in and hands something back, but not every rule of that shape earns the name function. This lesson settles which ones do, how such a rule is written down and evaluated, and what a graph of it can reveal at a glance.
- Combining and Composing Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
A discount takes some money off a price, then tax adds some back on. Two rules applied in a row behave like a single new rule, and rules can also be added or multiplied outright. This lesson builds new functions both ways, and asks whether swapping the order of a pair changes the result.
- Inverse Functions Advanced. This lesson goes beyond core Algebra I. You can skip it.
Shoes go on and come off; a door opens and closes. If a rule sends three to ten, is there a rule that sends ten back to three? This lesson follows that idea and asks what a rule must be like before it can be run backward at all.
- Defining New Operations Advanced. This lesson goes beyond core Algebra I. You can skip it.
Nothing stops you from inventing a symbol of your own and declaring what it does to a pair of numbers. Once it exists, the familiar questions return: does the order of the two inputs matter, does grouping change anything, and is there a number that leaves the other one unchanged?