Review III

Review III - Review for MAC 1140 Exam 3 1(L14 Which of the following equations is ’odd’(a f x = 2 x ± 1(b f x = 1 p x 2 5(c f x = x 3 ± x(d f

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Review for MAC 1140 Exam 3 1. (L14) Which of the following equations is ’odd’? (a) f ( x ) = 2 x ± 1 (b) f ( x ) = 1 p x 2 + 5 (c) f ( x ) = x 3 ± x (d) f ( x ) = j x j (ans. b and d are even, c is odd). 2. (L14) Match the graph with its polynomial function, y = (a) 2 x 3 ± 3 x + 1 (b) ± 1 3 x 3 + x 2 ± 4 3 (c) 1 5 x 5 ± 2 x 3 + 9 5 x (d) ± 1 5 x 5 ± 2 x 3 + 9 5 x (ans. (c)) 3. Given the graph below, is the degree of the polynomial even or odd? Is the leading coe±cient a n positive or negative? Construct a possible polynomial that matches the graph and the given points. (ans. f ( x ) = x 2 ( x + 4)( x ± 4), answer is not unique)

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4. (L14) Sketch h ( x ) = ± 1 3 x ( x ± 4) 2 , determine the end behavior and intercepts, zeros, and multiplicities. (ans. rises to the left, falls to the right; x ± intercept at x = 0(1) ; 4(2); y ± int : y = 0) 5. (L14) Sketch g ( x ) = ± 5 x 2 ± x 3 , how many turning points does the graph have? (ans. 2 turning points) 6. (L14) Find all zeros of g ( x ) = 2( x 3 ± 9 x )( x + 3) 3 ( x 2 + 4) 3 and their multiplicities and determine if graph touches or cross at the zeros; also ±nd the intercepts and end behavior. (ans.zeros: x = ± 3(4) touch; 0(1) corss; 3(1) cross ), x ± int: x = ± 3 ; 0 ; 3; y ± int: y = 0; end behavior: rises on both sides.
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This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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Review III - Review for MAC 1140 Exam 3 1(L14 Which of the following equations is ’odd’(a f x = 2 x ± 1(b f x = 1 p x 2 5(c f x = x 3 ± x(d f

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