Building Functions Feedback Functions Inverses

Finding Inverse Functions





What can we say that this student does or does not understand about inverse functions?

Functions High School: Functions Interpreting Functions Uncategorized


tina infinity


The question asked for the range of the function SQRT(x).  What are your thoughts about the way the student answered the question. What does it show about what this particular student knows.*

In the past, I’ve publicly kvetched about how the only questions that we grapple with on this blog are about the particularities, rather than the generalities, of student work. This is a time when I think that the most interesting questions are accessed through thinking about what this particular kid was thinking. I’d also be interested in hearing how you think this represents a trend in students’ thinking, in general.

Thanks to Tina for the submission!

Building Functions Inverses

One inverse functions problem, many mistakes

precalc 23

precalc 23 2precalc 23 3 precalc 23 4 precalc 23 5

You grade these tests on Sunday, and you see these kids on Monday. What does the lesson plan look like?

For more context and analysis, go check out the blog from whence these came.

Functions Graphing Interpreting Functions Uncategorized

A Contest!


Marshall Thompson is offering a substantial bounty for the correct explanation for this mistake. (He knows the truth from talking to the student.)

Who’s got it?

Functions Interpreting Functions

Range of a Function


Bob Lochel writes:

“I used this question as part of a benchmark assessment given to over 1,100 students at our high school, as preparation for the state test.  Only 14% of students gave the correct answer B, while 66% of students chose A as their response.  I’m not surprised that students would perform weakly on a domain/range question, but I am surprised that so many chose A.  I featured this problem as a set-up for a domain and range activity on my blog:, but feel free to share it with the mathmistakes crowd.”

So, what do we think about choosing A? Any theories?

Building Functions Functions

Composition of Functions

In the comments, say something. If you’re looking for a prompt, how about “Give a theory as to why this kid made the mistake that he did.”

Building Functions Functions High School: Functions

Inverse Functions

What does the student know, and what does he misunderstand? How would you help?

Today’s submission comes via Christopher Danielson, who blogs at Overthinking my teaching.

Functions Interpreting Functions

Function Notation

How do you teach function notation? How would you help your students avoid this sort of mistake?

F-BF.1 Functions

Keeping your composure (? does that even count as a pun?)

What does this student know about composition of functions?

What’s going through the kid’s brain when he makes his mistake?

How would you help?

Algebra 2 F-BF.1 Functions

Composition of Functions

This kid clearly knows some of the basics of composing functions. But check out that last line.




What is going through this kid’s brain, and how would you respond?