Pre-Calculus Practice Problem 71

Pre-Calculus Practice Problem 71 - equation? How would this...

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Unit 2, Activity 6, Rational Functions and their Graphs with Answers Blackline Masters, Advanced Math-Pre-Calculus Page 69 Louisiana Comprehensive Curriculum, Revised 2008 PART II 1. What symmetry do you see in the graphs drawn in Part I? (Think in terms of even and odd functions) #1 and #2 are even functions 2. The double zero in #2 caused the tangency to the x -axis. What can we do to #5 to make its “parabola” tangent to the x -axis? How would this change your answers to this question? Rewrite the function to be 8 6 3 ) ( 2 2 + = x x x x f . The horizontal asymptote will now be y = 3. 3. None of these graphs had “holes” because of discontinuities. Suppose I want the discontinuity in #3 to be a hole rather than asymptotic. How should I change the
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Unformatted text preview: equation? How would this change the graph? Add (x + 4) as a factor in the numerator. The function is now 4 ) 4 )( 4 2 ( ) ( + + + = x x x x f and the graph would be the line y = 2x + 4 with a hole at (-4, -4). 4. Which of the problems above have a range that is the set of all reals? How can you tell from the graph? . Problem # 4 has a range that is the set of all reals. For + + ) ( , 3 x f x and for ) ( , 2 x f x 5. Write an equation for a rational function that has (a) at least one zero, (b) two vertical asymptotes and one hole, and c) a horizontal asymptote other than 0. Hand it to another student to solve. One example would be 4 4 4 ) ( 2 3 2 3 + + = x x x x x x f...
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