Grade 12 · Theory
Function notation and transformations
Functions and inverses · about 3 min
Visual overview: Function notation and transformations1 MIN READ
2 study sections · pause after each one and recall the key ideaFunction notation is a precise language, and transformations let you predict a graph without plotting it.
Key points- f(x) is the output for input x; f(2) means substitute 2.
- f(x) + q shifts vertically; f(x − p) shifts horizontally.
- −f(x) reflects in the x-axis; f(−x) reflects in the y-axis.
- a·f(x) stretches vertically by a factor of a.
- Transformation — a shift, reflection or stretch of a graph.
EXAM TIP
horizontal shifts work opposite to intuition — f(x − 3) moves the graph 3 units RIGHT.