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Graphing Rational Functions Date_____ Period____ Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each.
Determining how the graph approaches the asymptotes: In a rational function, we have vertical asymptotes when the denominator equals 0 while the numerator does not.
10. vertical asymptotes x−3 1 2 2 2 3 2 2 Answers Advanced Functions Rational Rational Vertical Asymptotes 1. x=0 2. x=0 3. x=−1 4. a No vertical symp to e 5. x=0 6. x=0 7. x=0 8. x=1 9. N o vertical a symp te 1 0. x=3. Title: Rational Rational Vertical Asymptotes Worksheets Created Date:
To nd vertical asymptotes, we notice that the function is the result of multiplica-tion/division of polynomial and square root functions none of which have vertical asymptotes of their own. So the only possible vertical asymptotes may be found where the denominator of the function becomes zero: vertical asymptote at x = 2? To ensure. lim = 1.
Find the vertical and horizontal asymptotes of the function given below. (1) f(x) = -4/(x 2 - 3x) Solution (2) f(x) = (x-4)/(-4x-16) Solution
Describe any holes and/or vertical asymptotes for the graph of 𝑓. c. Explain how your answer from part b would change if the multiplicities of the zeros at 𝑥3 in the numerator and denominator were not equal?
Find the horizontal asymptotes of each function, if any, by set- ting up and evaluating limits at infinity and negative infinity. Enter the word 'none' if the function has no horizontal asymp- totes. Complete this problem on paper first so you can practice writing limit notation. (HINT: You only need to consider the terms with the highest
