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ca_m5

# ca_m5 - MAC 1105 Module 5 Transformation of Graphs Rev.S08...

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Rev.S08 MAC 1105 Module 5 Transformation of Graphs

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Rev.S08 2 Learning Objectives Upon completing this module, you should be able to: 1. Recognize the characteristics common to families of functions. 2. Evaluate and graph piecewise-defined functions. 3. Identify vertical and horizontal asymptotes. 4. Graph functions using vertical and horizontal translations. Graph functions using stretching and shrinking. Graph functions using reflections. Combine transformations. Determine if a function is odd, even, or neither. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
Rev.S08 3 Transformation of Graphs http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. - - A Library of Functions A Library of Functions - - Transformation of Graphs Transformation of Graphs There are two major topics in this module:

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4 Rev.S08 What are Power Functions? http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Power functions typically have rational exponents . A special type of power function is a root function . Examples of power functions include: f 1 ( x ) = x 2 , f 2 ( x ) = x 3/4 , f 3 ( x ) = x 0.4 , and f 4 ( x ) =
5 Rev.S08 What are Power Functions? (Cont.) http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Often, the domain of a power function f is restricted to nonnegative numbers . Suppose the rational number p/q is written in lowest terms. The the domain of f ( x ) = x p/q is all real numbers whenever q is odd and all nonnegative numbers whenever q is even . The following graphs show 3 common power functions.

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6 Rev.S08 What are Polynomial Functions? Polynomial functions are frequently used to approximate data. A polynomial function of degree 2 or higher is a nonlinear function. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.
7 Rev.S08 Next, let’s look at the characteristics of different types of polynomial functions. http://faculty.valenciacc.edu/ashaw/ Click link to download other modules.

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8 Rev.S08 Constant Polynomial Functions http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. * No x -intercepts. * No turning points.
9 Rev.S08 Linear Polynomial Functions http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Degree 1. One x -intercepts. No turning points.

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10 Rev.S08 Quadratic Polynomial Functions http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Degree 2 - parabola that opens up or down. Zero, one or two x -intercepts. Exactly ONE turning point , which is also the VERTEX .
11 Rev.S08 Cubic Polynomial Functions http://faculty.valenciacc.edu/ashaw/ Click link to download other modules. Degree 3. Up to three x-intercepts. Up to two turning points.

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Rev.S08 12 What is a Piecewise-Defined Function?
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