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f(x) = 7²2²9

f(x) = 7²2²9

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Use the six-step procedure to graph the following rational function(show your work)

The function provided is \( f(x) = \frac{2}{x^2 - 9} \). ### Explanation: This is a rational function where: - The numerator is a constant: 2. - The denominator is a quadratic expression: \( x^2 - 9 \). ### Notes: - This function has vertical asymptotes where the denominator equals zero. Solving \( x^2 - 9 = 0 \) gives \( x = \pm 3 \). - These asymptotes represent values that \( x \) cannot take, as they would make the denominator zero, leading to division by zero. - The function may also have a horizontal asymptote, determined by comparing the degrees of the polynomial in the numerator and the denominator. In this case, the horizontal asymptote is \( y = 0 \) because the degree of the numerator is less than the degree of the denominator. Understanding these asymptotic behaviors is crucial for graphing and analyzing the function.
Transcribed Image Text:The function provided is \( f(x) = \frac{2}{x^2 - 9} \). ### Explanation: This is a rational function where: - The numerator is a constant: 2. - The denominator is a quadratic expression: \( x^2 - 9 \). ### Notes: - This function has vertical asymptotes where the denominator equals zero. Solving \( x^2 - 9 = 0 \) gives \( x = \pm 3 \). - These asymptotes represent values that \( x \) cannot take, as they would make the denominator zero, leading to division by zero. - The function may also have a horizontal asymptote, determined by comparing the degrees of the polynomial in the numerator and the denominator. In this case, the horizontal asymptote is \( y = 0 \) because the degree of the numerator is less than the degree of the denominator. Understanding these asymptotic behaviors is crucial for graphing and analyzing the function.
Expert Solution
Step 1: Given function

f left parenthesis x right parenthesis equals fraction numerator 2 over denominator x squared minus 9 end fraction

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