Compressions And Stretches | College Algebra - Lumen Learning

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Module 6: Algebraic Operations on Functions

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Compressions and Stretches

Learning Outcomes

  • Graph Functions Using Compressions and Stretches.

Adding a constant to the inputs or outputs of a function changed the position of a graph with respect to the axes, but it did not affect the shape of a graph. We now explore the effects of multiplying the inputs or outputs by some quantity.

We can transform the inside (input values) of a function or we can transform the outside (output values) of a function. Each change has a specific effect that can be seen graphically.

Vertical Stretches and Compressions

When we multiply a function by a positive constant, we get a function whose graph is stretched or compressed vertically in relation to the graph of the original function. If the constant is greater than 1, we get a vertical stretch; if the constant is between 0 and 1, we get a vertical compression. The graph below shows a function multiplied by constant factors 2 and 0.5 and the resulting vertical stretch and compression.

Graph of a function that shows vertical stretching and compression.

Vertical stretch and compression

A General Note: Vertical Stretches and Compressions

Given a function [latex]f\left(x\right)[/latex], a new function [latex]g\left(x\right)=af\left(x\right)[/latex], where [latex]a[/latex] is a constant, is a vertical stretch or vertical compression of the function [latex]f\left(x\right)[/latex].

  • If [latex]a>1[/latex], then the graph will be stretched.
  • If [latex]0 < a < 1[/latex], then the graph will be compressed.
  • If [latex]a1[/latex], the graph is stretched by a factor of [latex]a[/latex]. If [latex]{ 0 }

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