Question
upstudy study bank question image url

Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph of \( \mathrm{f}(\mathrm{x})=\frac{\mathrm{x}+9}{\mathrm{x}-9} \). Find the intervals where \( \mathrm{f}(\mathrm{x}) \) is concave upward or downward. Select the correct choice below and fill in the answer box(es) to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed.) A. The function is concave upward on B. The function is concave downward on is never concave downward. It is never concave upward. C. The function is concave upward on \( \square \). It is concave downward on \( \square \). Find the iocation of any inflection points of \( \mathrm{f}(\mathrm{x}) \). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. There is an inflection point at \( \mathrm{x}=\square \). (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no inflection points.

Ask by Perkins Estrada. in the United States
Mar 17,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The function \( f(x) = \frac{x+9}{x-9} \) is concave upward on \( (9, \infty) \) and concave downward on \( (-\infty, 9) \). There are no inflection points.

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 sketch the graph of \( f(x) = \frac{x+9}{x-9} \), we start by identifying key features. The vertical asymptote occurs at \( x = 9 \) (where the denominator is zero), and the horizontal asymptote is at \( y = 1 \) (as \( x \) approaches infinity). The function intersects the y-axis at \( (0, -1) \) and the x-axis at \( (-9, 0) \). The graph will approach these asymptotes but never cross them. Now, for the concavity, we find the second derivative of \( f(x) \) and analyze its sign. The function is concave upward when the second derivative is positive and concave downward when it is negative. After computation, we conclude that the function is concave upward on \( (-\infty, 9) \) and concave downward on \( (9, \infty) \). Finally, regarding inflection points, there is only one at \( x = 9 \), which is where the concavity changes. So in conclusion: A. The function is concave upward on \( (-\infty, 9) \). B. The function is concave downward on \( (9, \infty) \). A. There is an inflection point at \( x = 9 \).

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