review2 - Outlines Function difference f f x h f x...

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Math 110 FS 2008 Review for Exam 2 Lecture #16 Exam 2 outlines. Outlines. 1. Functions. Definition of a function. Vertical line test. Domain. Range. Value at fixed point. ( 29 ( 29 ( 29 ( 29 , 0. Function difference f f x h f x Difference quotient f x h f x f h x h = + - + - = 2. Piecewise-Defined Functions. Value at given point. 3. Basic elementary functions. 4.Transformations of graphs. Order of transformations. Domain and Range of transformed functions. 5. Rational Functions. Reciprocal function ( 29 1 f x x = . Domain. Vertical asymptote of the ( 29 1 f x x = . Transformations (especially, horizontal shifts) of the reciprocal functions. Domain and vertical asymptote for transformed functions. Domain and Vertical Asymptotes of Rational Functions. 6. Direct and inverse variation with powers. 7. Quadratic Functions. Two forms of the equation: general and standard. 6. Properties of Quadratic Functions and their graphs: Domain. Range. Vertex. X -intercepts. Y- intercept. Maximum/minimum value of a Quadratic Function. Transformations of the graphs of Quadratic Functions. Axis of symmetry. 7. Applications of Quadratic Functions: max area enclosed, word problems about max/min value of a quadratic function. 8. Polynomial Functions. Definition. Degree. “Leading coefficient test”. “End behavior”. Y - intercept. X -intercepts. Multiplicity of zeros and patterns of x -intercepts. 1
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Math 110 FS 2008 Review for Exam 2 Lecture #16 Problem #1. Find the Domain of ( 29 6 5 f x x = - . Show your work. Write your answer using the interval notation. Problem #2. Find the Domain of ( 29 5 6 f x x = - - . Show your work. Write your answer using the interval notation. Problem #3. Find the Domain of ( 29 3 4 f x x = - . Show your work. Write your answer using the interval notation. Problem #4. Find the Domain of ( 29 2 2 11 12 x f x x x - = - - . Show your work. Write your answer using the interval notation. State vertical asymptotes. Problem #5. Find the Domain of ( 29 ( 29 2 15 11 12 f x x x x = + - . Show your work. Write your answer using the interval notation. State vertical asymptotes. Problem #6. Find the Domain of ( 29 2 3 2 7 x f x x x + = - + . Show your work. Write your answer using the interval notation. State vertical asymptotes. 2
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Math 110 FS 2008 Review for Exam 2 Lecture #16 Problem #7. Given ( 29 2 5 7 g x x x = - , find a) ( 29 ( 29 4 4 , 0 g h g h h + - b) ( 29 ( 29 , 0 g a h g a h h + - c) ( 29 ( 29 , 0 g x h g x h h + - d) ( 29 ( 29 1 1 , 0 g h g h h + - Problem #8. Given ( 29 1 7 g x x = + , find a) ( 29 ( 29 5 5 , 0 g h g h h - + - - b) ( 29 ( 29 2 2 , 0 g h g h h - + - - 3
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Math 110 FS 2008 Review for Exam 2 Lecture #16 Problem # 9. a) For ( 29 2 5 8 1 f x x x = - - - find the vertex algebraically, without using the graph of f . Show all steps of your computation.
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