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Stretching and Shrinking
Stretching and shrinking refer to transformations that alter how compact a function looks in the x or y direction.
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 yaxis, or vertically. If$b<1$ , the graph shrinks with respect to the yaxis.  In general, a horizontal stretch is given by the equation
$y = f(cx)$ . If$c>1$ , the graph shrinks with respect to the xaxis, or horizontally. If$c<1$ , the graph stretches with respect to the xaxis.
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 x or y by a constant, respectively.
Vertical Scaling
First, lets 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: Inverse Variation, Graphing Quadratic Equations in Vertex Form, 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: Solving Differential Equations, Visualizing Domain and Range, and The Vertical Line Test
 graph
 Appears in these related concepts: Reading Points on a Graph, Graphing Equations, and Graphical Representations of Functions
 independent variable
 Appears in these related concepts: Experimental Design, Converting between Exponential and Logarithmic Equations, and Experimental Research
 variable
 Appears in these related concepts: What is a Linear Function?, Math Review, and Introduction to Variables
 xaxis
 Appears in these related concepts: Translations, Basics of Graphing Polynomial Functions, and The Cartesian System
 yaxis
 Appears in these related concepts: Graphing Quadratic Equations In Standard Form, Reflections, and What is a Quadratic Function?
Sources
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Cite This Source
Source: Boundless. “Stretching and Shrinking.” Boundless Algebra. Boundless, 17 Jun. 2016. Retrieved 27 Jul. 2016 from https://www.boundless.com/algebra/textbooks/boundlessalgebratextbook/functions4/transformations31/stretchingandshrinking1201623/