Question
upstudy study bank question image url

Graph all vertical and horizontal asymptotes of the rational function. \[ f(x)=\frac{-6 x+11}{-2 x-9} \quad \text { Question } 7 \]

Ask by Simmons Rowe. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The vertical asymptote is \( x = -\frac{9}{2} \) and the horizontal asymptote is \( y = 3 \).

Solution

Sign in to Unlock Answers for Free!

A Learning Platform Trusted by Millions of Real Students and Teachers.

star-icon Unlock

Answered by UpStudy AI and reviewed by a Professional Tutor

Mind Expander

To find the vertical asymptote of the rational function \( f(x) = \frac{-6x + 11}{-2x - 9} \), we set the denominator equal to zero: \(-2x - 9 = 0\). Solving for \(x\), we get: \(-2x = 9 \Rightarrow x = -\frac{9}{2}\). Thus, the vertical asymptote is at \(x = -\frac{9}{2}\). To determine the horizontal asymptote, we compare the degrees of the numerator and denominator. Both have a degree of 1. The horizontal asymptote is found by taking the ratio of the leading coefficients. Thus, we have: Horizontal asymptote \(y = \frac{-6}{-2} = 3\). In summary, the vertical asymptote is at \(x = -\frac{9}{2}\) and the horizontal asymptote is at \(y = 3\).

Related Questions

Latest Pre Calculus Questions

Try Premium now!
Try Premium and ask Thoth AI unlimited math questions now!
Maybe later Go Premium
Study can be a real struggle
Why not UpStudy it?
Select your plan below
Premium

You can enjoy

Start now
  • Step-by-step explanations
  • 24/7 expert live tutors
  • Unlimited number of questions
  • No interruptions
  • Full access to Answer and Solution
  • Full Access to PDF Chat, UpStudy Chat, Browsing Chat
Basic

Totally free but limited

  • Limited Solution
Welcome to UpStudy!
Please sign in to continue the Thoth AI Chat journey
Continue with Email
Or continue with
By clicking “Sign in”, you agree to our Terms of Use & Privacy Policy