Concept Attainment Lesson F U N C T I O N S iMET Quads Loren Alldrin Terri Burke Sharmaine Grove Don Isbell Marlon Nance Instructions

WHAT IS A FUNCTION? Certain types of mathematical equations—and their resulting graphs—are called functions. All functions have one main characteristic in common. Looking at the examples to follow, can you figure out what it is?

NO YES

YES NO

YES NO

Have you spotted any similarities or characteristics that separate the “YES” graphs from the “NO” graphs? Here come some more examples…

YES NO

YES NO

Do you have an idea what distinguishes the “YES” graphs from the “NO” graphs? Write out your idea (your hypothesis) on the Functions Handout. Now, see if your hypothesis holds up in light of the remaining examples…

YES

NO

YES

Did your theory still hold true for the last examples? Did you have to change it to accommodate the new graphs? If necessary, revise your hypothesis and write it in the second box of your Functions Handout. Now it’s time to see if your hypothesis was correct.

In all the “YES” graphs, every value of X generates only one possible value for Y. YES NO X Y In the “NO” graphs, some values of X result in more than one value of Y. X Y Y

A mathematical equation that generates one distinct output (Y value) for every input (X value) is called a function. YES! X Y F U N C T I O N ? Y=sin(X)

On your Functions Handout, draw two graphs that might represent functions. Then, draw two that can’t represent functions. HEAD-SCRATCHER Could the graph of a function ever result in a vertical line?

End of presentation

INSTRUCTIONS This Concept Attainment lesson on Functions requires PowerPoint 2000 to be installed on your PC or Macintosh computer. This presentation includes animations within specific slides, with many of these self-timed. You control the pace of the overall delivery, however, by manually triggering some animations and advancing from one slide to the next. You can do this by clicking your mouse button or tapping the space bar on your keyboard. Back