Question
upstudy study bank question image url

ummarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( f(x)=\frac{x+3}{x-3} \) ind any horizontal asymptotes of \( f(x) \). Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one horizontal asymptote, \( \square \) (Type an equation.) B. The function has two horizontal asymptotes. The top asymptote is \( \square \) and the bottom asymptote is \( \square \) (Type equations.) . C. There are no horizontal asymptotes. nd any vertical asymptotes of \( f(x) \) Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function has one vertical asymptote, \( \square \) (Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \( \square \) and the rightmost asymptote is \( \square \) . (Type equations.) C. There are no vertical asymptotes.

Ask by Young Powell. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The function \( f(x) = \frac{x+3}{x-3} \) has one horizontal asymptote at \( y = 1 \) and one vertical asymptote at \( x = 3 \).

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

Bonus Knowledge

To summarize the pertinent information for the function \( f(x) = \frac{x+3}{x-3} \), we first analyze its horizontal and vertical asymptotes. As \( x \) approaches infinity, the highest degree terms dominate, leading to the horizontal asymptote at \( y = 1 \). So, the correct choice for horizontal asymptotes is A: The function has one horizontal asymptote, \( y = 1 \). Next, we determine the vertical asymptotes by identifying the values of \( x \) that make the denominator zero. Setting \( x - 3 = 0 \), we find a vertical asymptote at \( x = 3 \). Therefore, the correct choice for vertical asymptotes is A: The function has one vertical asymptote, \( x = 3 \). Now, you can easily sketch the graph—it's a hyperbola that approaches the horizontal asymptote (y=1) as x grows larger or smaller, and it will never touch the vertical asymptote at \( x=3 \). Happy graphing!

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