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Skip74 Write an equation for a rational function with: Vertical asymptotes at x = 1 and x = -3 x-intercepts at x = -6 and x = -5 y-intercept at 8 18(x + 5)(x + 6) y = (x - 1) (x +3) Question Help: D Video Message instructor

Skip74 Write an equation for a rational function with: Vertical asymptotes at x = 1 and x = -3 x-intercepts at x = -6 and x = -5 y-intercept at 8 18(x + 5)(x + 6) y = (x - 1) (x +3) Question Help: D Video Message instructor

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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**Task:** Write an equation for a rational function with: - **Vertical asymptotes** at \( x = 1 \) and \( x = -3 \) - **x-intercepts** at \( x = -6 \) and \( x = -5 \) - **y-intercept** at 8 **Solution:** To find a rational function \( y \) that meets these criteria, use the given conditions: Given \( y = \frac{18(x+5)(x+6)}{(x-1)(x+3)} \). - **Numerator \( 18(x+5)(x+6) \):** This part defines the x-intercepts at \( x = -6 \) and \( x = -5 \). The factor of 18 is used to adjust the y-intercept value to 8 (after substituting \( x = 0 \) into the function). - **Denominator \( (x-1)(x+3) \):** This part defines vertical asymptotes at \( x = 1 \) and \( x = -3 \). **Additional Features:** - **Question Help Options:** - **Video:** A link or resource for video help. - **Message Instructor:** An option to contact an instructor for assistance. **Submit Question Button:** Click to submit your answer for evaluation.
Transcribed Image Text:**Task:** Write an equation for a rational function with: - **Vertical asymptotes** at \( x = 1 \) and \( x = -3 \) - **x-intercepts** at \( x = -6 \) and \( x = -5 \) - **y-intercept** at 8 **Solution:** To find a rational function \( y \) that meets these criteria, use the given conditions: Given \( y = \frac{18(x+5)(x+6)}{(x-1)(x+3)} \). - **Numerator \( 18(x+5)(x+6) \):** This part defines the x-intercepts at \( x = -6 \) and \( x = -5 \). The factor of 18 is used to adjust the y-intercept value to 8 (after substituting \( x = 0 \) into the function). - **Denominator \( (x-1)(x+3) \):** This part defines vertical asymptotes at \( x = 1 \) and \( x = -3 \). **Additional Features:** - **Question Help Options:** - **Video:** A link or resource for video help. - **Message Instructor:** An option to contact an instructor for assistance. **Submit Question Button:** Click to submit your answer for evaluation.
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