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SAT Math: Function Transformations
31+ practice questions in Praczo
What you need to know
The concept, explained
- 1
Vertical shift: f(x) + k shifts the graph up k units; f(x) − k shifts it down.
- 2
Horizontal shift: f(x − h) shifts right h units; f(x + h) shifts left. (The sign inside is counterintuitive.)
- 3
Vertical stretch/compression: a·f(x) — if |a| > 1, stretch; if 0 < |a| < 1, compression.
- 4
Reflection: −f(x) reflects over x-axis; f(−x) reflects over y-axis.
- 5
Order of transformations matters when combining multiple shifts and stretches.
Common mistakes
- ✗ Horizontal shifts go in the opposite direction of the sign: f(x − 3) shifts RIGHT 3, not left.
- ✗ Confusing vertical and horizontal reflections — −f(x) flips up/down; f(−x) flips left/right.
Try a sample question
SAT-style practice
The graph of f(x) is shifted 3 units left and 2 units down. Which function represents the new graph?
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