9 - 105. does the general equation y = asin(x - h)+k allow for every possible transformation of the graph of…

9 - 105. does the general equation y = asin(x - h)+k allow for every possible transformation of the graph of y = sin(x)? are there any possible transformations other than the ones produced by varying values of a, h, and k? look back at the graphs you made for the swinging bag of blood in the first lesson of this chapter. discuss this with your team and be prepared to share your conjectures with the class.

9 - 105. does the general equation y = asin(x - h)+k allow for every possible transformation of the graph of y = sin(x)? are there any possible transformations other than the ones produced by varying values of a, h, and k? look back at the graphs you made for the swinging bag of blood in the first lesson of this chapter. discuss this with your team and be prepared to share your conjectures with the class.

Answer

Brief Explanation:

The equation $y = a\sin(x - h)+k$ allows for vertical stretch/compression ($a$), horizontal shift ($h$), and vertical shift ($k$) of the graph of $y=\sin(x)$. However, it does not account for horizontal stretch/compression (which would involve a coefficient of $x$ other than 1 inside the sine - function like $y = \sin(bx)$ where $b\neq1$).

Answer:

No, the general equation $y = a\sin(x - h)+k$ does not allow for every possible transformation of the graph of $y=\sin(x)$. There are possible transformations such as horizontal stretch or compression (by having a non - unit coefficient of $x$ inside the sine function) other than the ones produced by varying values of $a$, $h$, and $k$.