SAT Math: Transformations of Functions (Stretch & Compress)
15+ practice questions in Praczo
The concept, explained
- 1
Function transformations alter the shape or position of a graph without changing its fundamental type.
- 2
y = a * f(x) causes a vertical stretch if |a| > 1, and a vertical compression if 0 < |a| < 1. A negative "a" reflects the graph over the x-axis.
- 3
y = f(b * x) causes a horizontal compression if |b| > 1, and a horizontal stretch if 0 < |b| < 1. A negative "b" reflects over the y-axis.
- 4
Remember that horizontal changes (inside the parentheses) are often counter-intuitive: a multiplier of 2 makes it narrower (compressed), not wider.
- ✗ Confusing vertical shifts (adding outside) with vertical stretches (multiplying outside).
- ✗ Assuming that f(2x) makes the graph twice as wide, when it actually makes it half as wide.
SAT-style practice
If the graph of y = x² is transformed to y = (1/3)x², how does the new graph relate to the original?
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