Extend understanding of transformations to include functions (given in equation or graph form) in general, including horizontal and vertical translations, and horizontal and vertical stretches.
| (a) |
Compare and analyze various graphs of transformations of the function $y = f(x)$, and generalize about the effect of the placement of different coefficients on the original graph of $y = f(x)$. |
| (b) |
Develop, generalize, explain, and apply strategies for sketching transformations of the graph of $y = f(x)$ to give the graph of $y-k=af(b(x-h))$. |
| (c) |
Write the equation of a function that has undergone specified vertical translations, horizontal translations, vertical stretches, and/or horizontal translations of the function $y = f(x)$ for which the equation is given. |
