Refer to the resulting difficulties to emphasize the need for domain and range restrictions when dealing with exponential and logarithmic functions. As a follow up, discuss base e and natural logarithms. Use the graphing calculator to discuss the effects of changing A, B, C, and D on the graph of Provide students with real sinusoidal data. Ask them to graph the data, estimate the amplitude and suggest possible equations to represent the data. The data can then be entered into the graphing calculator and the sinusoidial regression function can be applied.
Students can compare the calculator results to their own predicted equation.
Alternatively use geometry software to model the relationships of the inscribed right angle and the change in the central angle. Use a graphing calculator or graphing software to match a given graph to a trigonometric equation. Given a solution, have students write a problem that matches it. Have students choose a number of equations from a list to make up their card, then graph equations on overhead until someone gets 5 in a row. Students should be able to demonstrate their knowledge of the relationship between logarithms and exponential functions, both in theory and in applications, in a variety of problem situations.