Question
upstudy study bank question image url

Find all horizontal and vertical asyinptoles of .

Find the horizontal asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one horizontal asymptote, ,
(Type an equation.)
B. The function has two horizontal asymptotes. The top asymptote is and the bottorn asymplote is
(Type equations.)
Find the vertical asymptotes. Select the correct choice and, if necessary, fill in the answer box(es) to complete your choice.
A. The function has one vertical asymptote, .
(Type an equation.)
B. The function has two vertical asymptotes. The leltriost asymptote is and the nightmost asymptole is
(Type equations)
C. The function has no vertical asymptotes.

Ask by Barker Cook. in the United States
Jan 22,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

Horizontal Asymptote:
Vertical Asymptotes: and

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

The Deep Dive

To find the horizontal asymptotes of the function , we start by noting the degrees of the numerator and the denominator. Both the numerator and denominator have a degree of 2. The horizontal asymptote is determined by the coefficients of the leading terms. Here, the leading coefficient of the numerator is 4 and that of the denominator is 1, so . Thus, the correct choice is:
A. The function has one horizontal asymptote, .
Next, for the vertical asymptotes, we need to find where the denominator equals zero, as these points typically indicate vertical asymptotes. The denominator is . Factoring this expression gives us , which means and are the locations of the vertical asymptotes. So, the correct choice is:
B. The function has two vertical asymptotes. The leftmost asymptote is and the rightmost asymptote is .

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