When we were working through our first trigonometry unit in Precalculus, I wanted students to be able to make the connection between the equation of the trig function and the graph. Before I'd ask students to graph the trig equations themselves, I wanted students to practice finding amplitude, frequency, period, midline, and phase shifts and be able to look for those in a graph. I found a card set of trig functions and their matching graphs on TES here...
There are three sets of functions and graphs, so I copied each set on a different color of paper. I had teams of students work with one color and when their matches were made correctly, they moved onto another color.
As I would check student matches, I'd ask questions such as: How did you decide that this graph matched with this equation? What part of the equation gives you a clue to how tall your graph will be? What's the difference between the frequency and period and how can you explain the difference using this graph and equation?
I know these concepts are all learned in Algebra 2, but students sure do need the refresher when they get to Precalculus.
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