3 types:
I want to convert this:
$$y=f(x) $$To the following function:
$$\begin{align} y=-af(-bx+c)d, \end{align} $$Here's how I can do this:
| Translation | Change in function |
|---|---|
| ----------- | ------------------ |
| Vertical Translation (+d) units parallel to the y-axis | y=f(x)+d |
| Horizontal Dilation of factor $\frac{1}{b}$ | y=f(bx) |
| Horizontal Translation of (c) units to the right. | y=f(x-c) |
| Vertical Dilation of factor (a) | y=af(x) |
| Reflection about the x-axis | y=-f(x) |
| Reflection about the y-axis | y=f(-x) |
