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Some highschools teach the following "false facts." 1. If the graph of f(x) has a horizontal asymptote at y = c then c is not in the range of f(x). 2. If the graph of f(x) has a horizontal asymptote at y = c then f(x) c for any x. Verify the following examples, which show the facts above are false. 1. Show that f(x) = 2. Show that g(x) = x2 x cos(x) x²+1 16 = 0 and 0 is contained in its range. has a horizontal asymptote at y has a horizontal asymptote at y = 0 and satisfies g(x) = 0 for many x. Find all such x.

Some highschools teach the following "false facts." 1. If the graph of f(x) has a horizontal asymptote at y = c then c is not in the range of f(x). 2. If the graph of f(x) has a horizontal asymptote at y = c then f(x) c for any x. Verify the following examples, which show the facts above are false. 1. Show that f(x) = 2. Show that g(x) = x2 x cos(x) x²+1 16 = 0 and 0 is contained in its range. has a horizontal asymptote at y has a horizontal asymptote at y = 0 and satisfies g(x) = 0 for many x. Find all such x.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 51E
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Some highschools teach the following "false facts." 1. If the graph of f(x) has a horizontal asymptote at y = c then c is not in the range of f(x). 2. If the graph of f(x) has a horizontal asymptote at y = c then f(x) c for any x. Verify the following examples, which show the facts above are false. 1. Show that f(x) = 2. Show that g(x) = x2 x cos(x) x²+1 16 = 0 and 0 is contained in its range. has a horizontal asymptote at y has a horizontal asymptote at y = 0 and satisfies g(x) = 0 for many x. Find all such x.
Transcribed Image Text:Some highschools teach the following "false facts." 1. If the graph of f(x) has a horizontal asymptote at y = c then c is not in the range of f(x). 2. If the graph of f(x) has a horizontal asymptote at y = c then f(x) c for any x. Verify the following examples, which show the facts above are false. 1. Show that f(x) = 2. Show that g(x) = x2 x cos(x) x²+1 16 = 0 and 0 is contained in its range. has a horizontal asymptote at y has a horizontal asymptote at y = 0 and satisfies g(x) = 0 for many x. Find all such x.
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