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8) Graph the function. Be sure to label all the asymptotes. List the domain and the x and y intercepts. a) f(x): = 1 x-5 b) f(x) = x² + 3x 2x3-5x2-3x

8) Graph the function. Be sure to label all the asymptotes. List the domain and the x and y intercepts. a) f(x): = 1 x-5 b) f(x) = x² + 3x 2x3-5x2-3x

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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Question
**Task 8**: Graph the function. Be sure to label all the asymptotes. List the domain and the x and y intercepts. a) \( f(x) = \frac{1}{x-5} \) b) \( f(x) = \frac{x^2 + 3x}{2x^3 - 5x^2 - 3x} \) *Instructions*: For each function, identify vertical and horizontal asymptotes by analyzing the denominator and numerator, respectively. Determine domain restrictions based on where the denominator is zero. Compute the x-intercepts by setting the numerator to zero and find the y-intercept by evaluating the function at \( x = 0 \), if applicable.
Transcribed Image Text:**Task 8**: Graph the function. Be sure to label all the asymptotes. List the domain and the x and y intercepts. a) \( f(x) = \frac{1}{x-5} \) b) \( f(x) = \frac{x^2 + 3x}{2x^3 - 5x^2 - 3x} \) *Instructions*: For each function, identify vertical and horizontal asymptotes by analyzing the denominator and numerator, respectively. Determine domain restrictions based on where the denominator is zero. Compute the x-intercepts by setting the numerator to zero and find the y-intercept by evaluating the function at \( x = 0 \), if applicable.
Expert Solution
Step 1: Introduction and definition of domain

a)  The rational function fx=1x-5

b) The rational function fx=x2+3x2x3-5x2-3x

Find the domain x, and y intercepts and graph the functions label all the asymptotes.

Domain: The domain is the set of all real numbers except where the function is undefined.

 

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