ca_m5_handouts

ca_m5_handouts - 1 Rev.S08 MAC 1105 Module 5 Transformation...

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Unformatted text preview: 1 Rev.S08 MAC 1105 Module 5 Transformation of Graphs 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. 5. Graph functions using stretching and shrinking. 6. Graph functions using reflections. 7. Combine transformations. 8. Determine if a function is odd, even, or neither. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Rev.S08 3 Transformation of Graphs ht p:/ 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: 2 4 Rev.S08 What are Power Functions? ht p:/ 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.) ht p:/ 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. 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. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. 3 7 Rev.S08 Next, lets look at the characteristics of different types of polynomial functions. ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. 8 Rev.S08 Constant Polynomial Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. * No x-intercepts. * No turning points. 9 Rev.S08 Linear Polynomial Functions ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules. Degree 1. One x-intercepts. No turning points. 4 10 Rev.S08 Quadratic Polynomial Functions ht p:/ 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 ht p:/ faculty.valenciacc.edu/ashaw/ Click link to download other modules....
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ca_m5_handouts - 1 Rev.S08 MAC 1105 Module 5 Transformation...

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