9. For each of the following parts, properties of a rational function are listed. Find an algebraic expression of the function and graph it. Include all asymptotes of the graph. (a) Rational function f. • f(-2) = 0. * f(x) → –∞ as x → –1- * f(x) → o as x → –1+ * f(x) → ∞ as x → 1- * f(x) → –∞ as x → 1+ • f(0) = 2. • The zeros of its numerator are -1 with multiplicity 2 and 3 with multiplicity 1. • The zeros of its denominator are -2 with multiplicity 1 and 4 with multiplicity 2. • It has one removable discontinuity at x = 1. • Its y-intercept is 1. (Ъ) • The zero of its numerator is 2 with multiplicity 2. • The zero of its denominator is 3 with multiplicity 1. • Its y-intercept is -. (c)

9. For each of the following parts, properties of a rational function are listed. Find an algebraic expression of the function and graph it. Include all asymptotes of the graph. (a) Rational function f. • f(-2) = 0. * f(x) → –∞ as x → –1- * f(x) → o as x → –1+ * f(x) → ∞ as x → 1- * f(x) → –∞ as x → 1+ • f(0) = 2. • The zeros of its numerator are -1 with multiplicity 2 and 3 with multiplicity 1. • The zeros of its denominator are -2 with multiplicity 1 and 4 with multiplicity 2. • It has one removable discontinuity at x = 1. • Its y-intercept is 1. (Ъ) • The zero of its numerator is 2 with multiplicity 2. • The zero of its denominator is 3 with multiplicity 1. • Its y-intercept is -. (c)

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section: Chapter Questions

Problem 11T: Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4x3+27 t(x)=x+2x39x u(x)=x225x2+x6...

See similar textbooks

Similar questions

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.
Find a rational function f that satisfies all the given properties vertical asymptote at x = 4 and horizontal asymptote at y = 0
Find a rational function which has a vertical asymptote ofx= 4, a horizontal asymptote ofy= 0,and ay-intercept of (0,7). (Note: there are infinitely many “right answers” to this problem.)
8-The rational function y=ax2/(bx2+(2b+1) x +b) has one verticalasymptote and passes through point (2, -3) determine the values of aand b.
3)For each of the following rational functions, determine where the vertical asymptote(s) of the function occur. If there is more than one vertical asymptote, enter your answer as a comma-separated list (like "1, 3"). If the function does not have a vertical asymptote, enter"DNE". (ONLY D,E, )
The following question is about the rational function r(x) = (x + 1)(x − 2) (x + 2)(x − 9) . The function r has horizontal asymptote y =