2.7.4

Stretches & Compressions

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Stretches and Compressions

Graphs of functions can be stretched or compressed in either the horizontal or vertical direction.

Illustrative background for Vertical stretches and compressionsIllustrative background for Vertical stretches and compressions ?? "content

Vertical stretches and compressions

  • Given a function f(x), a new function g(x) = af(x), where a is a constant, is a vertical stretch or vertical compression of the function f(x).
    • If a > 1, then the graph will be stretched.
    • If 0 < a < 1, then the graph will be compressed.
Illustrative background for Horizontal stretches and compressionsIllustrative background for Horizontal stretches and compressions ?? "content

Horizontal stretches and compressions

  • Given a function f(x), a new function g(x) = f(bx), where b is a constant, is a horizontal stretch or horizontal compression of the function f(x).
    • If b > 1, then the graph will be compressed by 1b\frac{1}{b}.
    • If 0 < b < 1, then the graph will be stretched by 1b\frac{1}{b}.

Jump to other topics

1Proof

2Algebra & Functions

2.1Powers & Roots

2.2Quadratic Equations

2.3Inequalities

2.4Polynomials

2.5Graphs

2.6Functions

2.7Transformation of Graphs

2.8Partial Fractions (A2 Only)

3Coordinate Geometry

4Sequences & Series

5Trigonometry

6Exponentials & Logarithms

7Differentiation

8Integration

9Numerical Methods

10Vectors

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