Key Concepts
- Functions can be shifted up, down, left, or right by adding/subtracting constants.
- Functions can be scaled or reflected by multiplying negative or fractional values.
Skills Covered
- Translating functions horizontally and vertically.
- Identifying reflection across the x-axis or y-axis.
- Identifying vertical and horizontal stretching or compression.
Example Problems
- Given (f(x) = x^2 + 5), write the equation of the function shifted $3$ units up.
- If (g(x) = f(x - 4) + 2), describe the transformation applied to (f(x)).
- Reflect (f(x) = x^2 - 4) across the x-axis.
- Given (g(x) = 2f(x)), explain how it changes the original function.