## Function Transformations as Composition

(A new question of the week) We have discussed transformations of functions and their graphs at length, but a recent question suggested a slightly different way to think about them.

(A new question of the week) We have discussed transformations of functions and their graphs at length, but a recent question suggested a slightly different way to think about them.

Last week we looked at what functions are; but many students wonder why it all matters. What makes them useful? What makes functions worth distinguishing from non-functions? Why do we make the distinction we do? We love “why” questions, because they make us think more deeply!

A recent question, from Anindita, touched on the relationship of functions, relations, and rules. I referred to several answers we’ve given, which I’d long planned to put into a post (or two). This is it! We’ll start with a set of questions about what functions are.

Last week, we looked at problems involving some number of people making some number of things in some amount of time. In a classic twist on this problem, we’ll now examine several variants starting with “If a hen and a half can lay an egg and a half …”. Can we make sense of half-eggs …

A popular kind of word problem tells us how many people (or cats, or hens, …) it takes to make some number of houses (or kill some number of mice, or lay some number of eggs) in some amount of time, and then asks us to fill in one of the blanks for a different …

How Many A’s Can Make This Many B’s in This Much Time? Read More »