Translations
- y = f(x) + a moves the graph up by a units (down if a is negative).
- y = f(x + a) moves the graph left by a units. Inside the bracket, the direction is the opposite of what you might expect: y = f(x − 2) moves it right by 2.
- y = (x − 2)² is y = x² moved 2 units right, so its turning point is (2, 0).
Reflections
- y = −f(x) reflects the graph in the x-axis: every y-value changes sign.
- y = f(−x) reflects the graph in the y-axis: every x-value changes sign.
Following a point
- If y = f(x) has a turning point at (3, 4):
- y = f(x) + 2 has it at (3, 6); y = f(x − 1) at (4, 4); y = −f(x) at (3, −4); y = f(−x) at (−3, 4).
Key terms
- Transformation
- A change to the position or shape of a graph.
- Translation
- Sliding a graph without turning or flipping it.
- Reflection
- Flipping a graph in a mirror line, such as an axis.
- f(x)
- Function notation for an expression in x, such as f(x) = x².
- Turning point
- The minimum or maximum point of a curve.