Timmy is learning about function transformations! For a function ~g(x)=af(k(x-d))+c~, ~g(x)~ is the graph of ~f(x)~, but
- Vertically stretched by a factor of ~a~
- Horizontally compressed by a factor of ~\frac 1k~
- Horizontally translated by ~d~ units right
- Vertically translated ~c~ units up
For this problem, you can assume that ~a~, ~d~, and ~c~ are all nonnegative integers, and ~k~ is a positive integer. Additionally, the numbers will always be present (even if they are redundant, such as when ~k=1~).
Can you help Timmy with his homework?
~0\le a,d,c\le 10^6~
One line with one string, a function of the form ~af(k(x-d))+c~
4 lines of the following form:
Vertically stretched by a factor of [a] Horizontally compressed by a factor of 1/[k] Horizontally translated by [d] units right Vertically translated [c] units up
Where each square bracket (
[n]) means that the number
n replaces the bracket (we do not include the square brackets)
Vertically stretched by a factor of 10 Horizontally compressed by a factor of 1/3 Horizontally translated by 4 units right Vertically translated 5 units up