Algebra for College Students

Algebra for College Students

10th Edition

ISBN: 9781285195780

Author: Jerome E. Kaufmann, Karen L. Schwitters

Publisher: Cengage Learning

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The graph of the rational function f(x) is shown below. Using the graph, determine which of the following local and end behaviors are correct. Select all correct answers. Select all that apply: As I →→→→∞0, f(1)→ −1 As I →→2¹, f(x) → ∞ As I →→→→2. f(x) → ∞ As I →→→→∞0, f(1) → 1 As I →→→2. f(x) → →∞ As I →→∞0, f(z) → −1 3- 1- 0 10

Transcribed Image Text:The graph of the rational function f(x) is shown below. Using the graph, determine which of the following local and end behaviors are correct. Select all correct answers. Select all that apply: As I →→→→∞0, f(1)→ −1 As I →→2¹, f(x) → ∞ As I →→→→2. f(x) → ∞ As I →→→→∞0, f(1) → 1 As I →→→2. f(x) → →∞ As I →→∞0, f(z) → −1 3- 1- 0 10

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If the rational function y=r(x) has the vertical asymptote x=2, then as x2+, either y or y.

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Consider the following rational functions: r(x)=x2x22x1 s(x)=x2+4×3+27 t(x)=x+2x39x u(x)=x225x2+x6 w(x)=x+3×3+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.

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