Stretches & Compressions

Maths: Edexcel A Level Pure Maths, topic 2.7.4

Stretches and Compressions

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

Vertical stretches and compressions

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.

Vertical stretches and compressions

Vertical stretches and compressions

Horizontal stretches and compressions

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 $\frac{1}{b}$ .
If 0 < b < 1, then the graph will be stretched by $\frac{1}{b}$ .

Horizontal stretches and compressions

Horizontal stretches and compressions

Test yourself on Stretches & Compressions

The equation of the solid line is x². Which is the correct equation for the dashed line?
The equation of the solid line is x². Which is the correct equation for the dashed line?
The equation of the solid line is x². Which is the correct equation for the dashed line?
The equation of the solid line is sin(x). Which is the correct equation for the dashed line?

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