Pre Calc research paper

 Summarize the main “concept image” components of inverse functions

described in the article (e.g. reflection, undoing, algebraic swap).

Algebraically swapping x and y to find the inverse, undoing the original function’s operation, and reflection across the y = x line (diagonal)

Identify and explain one common misconception or difficulty students have with

inverse functions, as discussed in the article.

Students tend to think all functions have an inverse, when infact they don’t a function must be 1-to-1 to have an inverse

The article contrasts “undoing” meaning vs “formal / algebraic” meaning of

inverse functions. Explain both and give an example of each.

Undoing is the literal inverse of functions e.g. x+5’s inverse would be x -5 and that is obviously wrong, the algebraic meaning is doing a function then its inverse would result with the original function

Choose one of your precalculus topics (say, “analyzing graphs of functions”) and

relate how misunderstandings about inverse functions can arise in that context,

using examples.

When analyzing graphs of functions students might think that a graph is flipped across the x or the y axis, when infact its flipped across the y = x line (diagonal line)

Propose one small classroom activity or question that might help students

reconcile their intuitive (concept image) understanding of inverse functions with

the formal definition

Give students a function and its inverse and let them graph both to see how they reflect across y = x