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Precalculus: A Unit Circle Approach (3rd Edition)
- Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3x3+6x+9x (a) Which of these rational functions has a horizontal asymptote? (b) Which of these functions has a slant asymptote? (c) Which Of these functions has no vertical asymptote? (d) Which Of these functions has a "hole"? (e) What are the asymptotes of the function r(x) ? (f) Graph y =u(x) , showing clearly any asymptote and x- and y intercepts the function may have. (g) Use long division to find a polynomial P that has the same end behavior as t. graph both P and t on the same screen to verify that they have the sane end behavior.arrow_forwardA polynomial of degree n I has exactly ____________________zero if a zero of multiplicity m is counted m times.arrow_forwardGiven a rational function f(x)=n(x)/d(x), then f(x) has a vertical asymptote at x=c if: A. n(c) = 0 B. d(c)= 0 C. d(c) = 0 and n(c) =/= 0 D. n(c) = 0 and d(c) =/= 0arrow_forward
- f(x) = (x2-x-1) e-x is restricted to the domain x ≥ 0 and it has two critical points. One at x = 0 and the other at x = 3 At what value x does f(x) attain its maximum?arrow_forwardConsider the function f(x) = -5x^2 + 6x - 7. f(x) has a critical point at x = A. Find the value of A A = ___arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage