Function Notation & Transformations
Understand f(x) notation and how to transform functions.
Practice Problems
g(x) = (x - 3)² + 2
f(x) = x², g(x) = -2x²
Pro Tips & Shortcuts
SAT Tip: f(x) is just another way to write y. They mean the same thing.
SAT Tip: Outside changes affect y-values (vertical). Inside changes affect x-values (horizontal).
SAT Tip: Horizontal shifts are opposite to what you might expect. f(x - 3) shifts RIGHT 3.
SAT Tip: Apply transformations in order: horizontal first, then vertical.
SAT Tip: Negative coefficient means reflection. Absolute value > 1 means stretch.
To evaluate f(3), replace every x with 3 in the function rule.
Think: adding to the output makes it bigger, shifting the graph up.
Think: f(x - 2) means 'what f was doing 2 units earlier' so shift right.
For vertex form a(x-h)² + k, vertex is at (h, k).
Coefficient outside affects steepness; negative flips the graph.