Secants, tangents, rotations, and reflections

Michael Brian Maltenfort*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given the graph of a continuous function on an interval, if we know the slopes of all the secant lines, then we can determine which rotations and reflections of the graph are also graphs of functions and, for those that are, whether the new functions are one-to-one. Provided that the original function is differentiable on the interior of the interval, we can determine the slopes of all secant lines by calculating the range of the function's derivative, provided that we know any subintervals where the function is linear.

Original languageEnglish (US)
Pages (from-to)24-34
Number of pages11
JournalCollege Mathematics Journal
Issue number1
StatePublished - Jan 1 2015

ASJC Scopus subject areas

  • Mathematics(all)
  • Education


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