D2.5

determine, through investigation using technology, the roles of the parameters $a$, $k$, $d$, and $c$ in functions of the form $y=af(k(x-d))+c$, where $f(x)=\sin x$ or $f(x)=\cos x$ with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of $f(x)=\sin x$ and $f(x)=\cos x$ (i.e., translations; reflections in the axes; vertical and horizontal stretches and compressions to and from the x- and y-axes) Sample problem: Investigate the graph $f(x)=2\sin (x-d)+10$ for various values of $d$, using technology, and describe the effects of changing $d$ in terms of a transformation.