11.5 Transformations of Functions

Transformations of Functions

1. 1. Describe and perform vertical translations $y = f(x) + c$ and horizontal translations $y = f(x - h)$.
2. 2. Describe and perform vertical dilations $y = a \cdot f(x)$ and horizontal dilations $y = f(ax)$.
3. 3. Describe and perform reflections in the $x$-axis ($y = -f(x)$) and in the $y$-axis ($y = f(-x)$).
4. 4. Apply a sequence of transformations to a graph and state the new key features.
5. 5. Match transformed graphs to their algebraic form, and vice versa.
6. 6. Use vertex form $y = a(x - h)^2 + k$ to read off translations and dilations of a quadratic.
7. 7. Apply transformations to known parent functions (linear, quadratic, exponential).