Big Ideas:
Changes to the values of A, B, h, and k in the general form of a trigonometric function, f(x)=A•sin[B(x-h)]+k, alter the graph of the function through both rigid and non-rigid transformations by changing the amplitude, midline, period, etc.
Students are presented with two transformed sinusoidal functions shown in contrasting ways. One function is given strictly by a view of a portion of its graph, while another is given by its algebraic equation, transformed in various ways. Students are then asked to compare key properties of these functions, including amplitude, period, and minimum value. Students should now be adept at analyzing a single sinusoidal function and understand that it has four representations: algebraic, graphical, numerical, and verbal. They are now tasked with moving between these representations fluidly while comparing features of two separate functions. This lesson is the culmination of the procedural study on transforming trigonometric functions, and students must use all the skills learned in previous lessons to succeed.
Vocabulary: sinusoidal function, function transformations, amplitude, period, frequency, midline, phase shift, extrema, minimum/maximum value
Special Materials:
No special material are needed for this lesson. Students may benefit from having access to graphing technology.