Questions tagged [functions]

For questions about the teaching of the function concept, function properties, and various types of functions.

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9
votes
3answers
507 views

What are some common ways students get confused about finding an inverse of a function?

What are some common ways students get confused about finding an inverse of a function? One I can think of is conflating multiplicative inverses of rational numbers with functional inverses. e.g. ...
18
votes
4answers
546 views

“Function” vs “Function of …”: how much does it contribute to students difficulties?

Most textbooks I've seen (and teachers I've met, myself included) are rather careless about the distinction between variables and functions. For example, when we write $y=f(x)$ we all know that $f$ ...
44
votes
21answers
6k views

How to help new students accept function notation

I am struggling to help some of my new precalculus students accept function notation -- something new to them this term. I am looking for strategies to help them adopt this new notation. Their main ...
24
votes
5answers
2k views

What is the proper way to ask a “find the domain” question?

A function is not really a function unless it's defined everywhere on its domain. So consider these three questions: Let $f: \mathbb{R} \rightarrow \mathbb{R}$ be the square root function $f(x) = \...
27
votes
12answers
3k views

Should we teach functions as sets of ordered pairs?

The context of this question is an "introduction to proofs and mathematics" class for freshman/sophomore math majors. Most textbooks for such a class say something about functions between arbitrary ...
7
votes
6answers
536 views

Simple, elegant ways to teach the idea of what functions are for the first time

The context In my country, when the concept of function needs to be introduced in math classes, most teachers will simply talk about $f(x)=c$, $f(x)=ax+b$ and $f(x)=1/x$ (constant, linear and inverse ...
6
votes
4answers
359 views

Is simplifying a rational function considered as a continuous extension?

Given the rational function $f(x)=\frac{x^2-1}{x+1}$. The expression can be simplified to $g(x)=x-1$ and thus the singularity at $x=-1$ is removed. I would personally claim that $f$ and $g$ are the ...
13
votes
4answers
852 views

Simpler explanation for finding the vertex of a parabola

I'm tutoring a Grade 11 Math student in BC, Canada, and we're going over parabolas. He's having difficulty with finding the vertex of a parabola - not how to find it, but WHY it works. And I'm having ...
12
votes
2answers
474 views

Why don't we teach codomains of functions in high school?

When I was a university student, I learnt that a function is the data of three informations: the rule that tells how to associate an object $x$ to its image $f(x)$, A domain $E$ where live the ...
8
votes
4answers
875 views

Shifting function graphs: writing vertical offset on the y-side?

Students tend to mix up signs when shifting function graphs around: consider $y=x^2$. To shift it one unit upwards ("increasing $y$"), you write $y=x^2+1$, to shift it to the right ("increasing $x$"), ...
3
votes
1answer
124 views

Dissemination of mistakes in international texts such as the IGCSE

I started tutoring IGCSE Mathematics. In preparation for just a 1 hour class for 1 student, I noticed at least 3 mistakes (confirmed with their replies to me) in Chapter 21 of the Haese 0607 book (...