Alternatively, students can do the exploration as homework and bring their observations to class for a whole class discussion and to pull together all the pieces. Students can work in class, possibly in groups, to experiment with the applet and then discuss their observations. The task can be used in a variety of ways. Even though the task statement only considers transformation of $y=\sin x$ it would be easy to change the applet and the problem statement to also explore transformations of $y=\cos x$. Sinusoidal functions are the perfect type of function to illustrate how new functions can be built from already known functions by shifting and scaling. It uses a desmos applet to let students explore the effect of changing the parameters in $y=A\sin(B(x-h))+k$ on the graph of the function. This task serves as an introduction to the family of sinusoidal functions. In the last row of the table, use the data you have collected to infer a general relationship between $B$ and the period.
Experiment with different values of $B$ and fill in the corresponding period in the table below.
There seems to be a relationship between $B$ and the period of the function but it is harder to describe than the other parameters.Describe how changing $A$, $k$, and $h$ changes the graph of the function.Add more rows to the table, if necessary. Then describe the effect that changing each parameter has on the shape of the graph. Use the sliders in the applet to change the values of $A,\ k,\ h,$ and $B$ to create the functions in the table.A general sinusoidal function is of the form $$y=A\sin(B(x-h))+k$$ or $$y=A\cos(B(x-h))+k.$$ In this task we will explore the effect that changing the parameters in a sinusoidal function has on the graph of the function.
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