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Stretching and Shrinking
Stretching and shrinking refer to transformations that alter how compact a function looks in the
Learning Objective

Manipulate functions so that they stretch or shrink
Key Points
 When by either
$f(x)$ or$x$ is multiplied by a number, functions can "stretch" or "shrink" vertically or horizontally, respectively, when graphed.  In general, a vertical stretch is given by the equation
$y=bf(x)$ . If$b>1$ , the graph stretches with respect to the$y$ axis, or vertically. If$b<1$ , the graph shrinks with respect to the$y$ axis.  In general, a horizontal stretch is given by the equation
$y = f(cx)$ . If$c>1$ , the graph shrinks with respect to the$x$ axis, or horizontally. If$c<1$ , the graph stretches with respect to the$x$ axis.
Term

scaling
A transformation that changes the size and/or shape of the graph of the function.
Full Text
In algebra, equations can undergo scaling, meaning they can be stretched horizontally or vertically along an axis. This is accomplished by multiplying either
Vertical Scaling
First, let's talk about vertical scaling. Multiplying the entire function
where
As an example, consider the initial sinusoidal function presented below:
If we want to vertically stretch the function by a factor of three, then the new function becomes:
Horizontal Scaling
Now lets analyze horizontal scaling.
Multiplying the independent variable
where
As an example, consider again the initial sinusoidal function:
If we want to induce horizontal shrinking, the new function becomes:
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Key Term Reference
 Scaling
 Appears in these related concepts: Transformations of Functions, Types of Conic Sections, and Introduction to Ellipses
 constant
 Appears in these related concepts: Graphing Quadratic Equations in Vertex Form, Inverse Variation, and Direct Variation
 equation
 Appears in these related concepts: Equations and Inequalities, Graphs of Equations as Graphs of Solutions, and What is an Equation?
 factor
 Appears in these related concepts: Rational Algebraic Expressions, Finding Factors of Polynomials, and Factors
 function
 Appears in these related concepts: The Vertical Line Test, Visualizing Domain and Range, and Solving Differential Equations
 graph
 Appears in these related concepts: Graphical Representations of Functions, Graphing Equations, and Reading Points on a Graph
 independent variable
 Appears in these related concepts: The Cartesian System, What is a Quadratic Function?, and Converting between Exponential and Logarithmic Equations
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
Sources
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Cite This Source
Source: Boundless. “Stretching and Shrinking.” Boundless Algebra. Boundless, 04 Oct. 2016. Retrieved 25 Oct. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/functions4/transformations31/stretchingandshrinking1201623/