Results 1 to 3 of 3

Thread: Given f(x) = (6x)/(x^2 - 9), find intercepts, asymptotes, limits, intervals of...

  1. #1
    New Member
    Join Date
    Nov 2017
    Location
    Halifax
    Posts
    1

    Given f(x) = (6x)/(x^2 - 9), find intercepts, asymptotes, limits, intervals of...

    Stuck with problem. Can someone please help?

    Answer the following questions regarding the function below, and use your answers to sketch the function.

    . . . . .[tex]f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}[/tex]

    1. List the x-values of any x-intercepts of f.

    2. Give the y-value of the y-intercept of f.

    3. List the x-values of any vertical asymptotes of f.

    4. Evaluate the following limits:


    . . . . .[tex]\displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)[/tex]

    . . . . .[tex]\displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)[/tex]

    5. List the y-values of any horizontal asymptotes of f.

    6. Find the intervals on which f is increasing or decreasing.

    7. List the coordinates of any local extrema.

    8. Find the intervals on which f is concave up or concave down.

    9. List the coordinates of any points of inflection.
    Attached Images Attached Images
    Last edited by stapel; 11-15-2017 at 07:16 PM. Reason: Typing out the text in the graphic; creating useful subject line.

  2. #2
    Elite Member
    Join Date
    Jun 2007
    Posts
    17,058
    Quote Originally Posted by onty5577 View Post
    Stuck with problem. Can someone please help?

    Answer the following questions regarding the function below, and use your answers to sketch the function.

    . . . . .[tex]f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}[/tex]

    1. List the x-values of any x-intercepts of f.

    2. Give the y-value of the y-intercept of f.

    3. List the x-values of any vertical asymptotes of f.

    4. Evaluate the following limits:


    . . . . .[tex]\displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)[/tex]

    . . . . .[tex]\displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)[/tex]

    5. List the y-values of any horizontal asymptotes of f.

    6. Find the intervals on which f is increasing or decreasing.

    7. List the coordinates of any local extrema.

    8. Find the intervals on which f is concave up or concave down.

    9. List the coordinates of any points of inflection.
    What are your thoughts?

    Please share your work with us ...even if you know it is wrong.

    If you are stuck at the beginning tell us and we'll start with the definitions.

    You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

    http://www.freemathhelp.com/forum/announcement.php?f=33
    Last edited by stapel; 11-15-2017 at 07:16 PM. Reason: Copying typed-out graphical content into reply.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

  3. #3
    Elite Member stapel's Avatar
    Join Date
    Feb 2004
    Posts
    15,519

    Cool

    Quote Originally Posted by onty5577 View Post
    Stuck with problem. Can someone please help?
    At which point are you stuck? How are you stuck?

    Quote Originally Posted by onty5577 View Post
    Answer the following questions regarding the function below, and use your answers to sketch the function.

    . . . . .[tex]f(x)\, =\, \dfrac{6x}{x^2\, -\, 9}[/tex]

    1. List the x-values of any x-intercepts of f.

    2. Give the y-value of the y-intercept of f.
    Finding intercepts is just algebra. (here) Where are you getting bogged down in the plugging-zero-in-and-solving process?

    Quote Originally Posted by onty5577 View Post
    3. List the x-values of any vertical asymptotes of f.

    4. Evaluate the following limits:


    . . . . .[tex]\displaystyle \mbox{a. }\, \lim_{x \rightarrow \infty}\, f(x)[/tex]

    . . . . .[tex]\displaystyle \mbox{b. }\, \lim_{x \rightarrow -\infty}\, f(x)[/tex]

    5. List the y-values of any horizontal asymptotes of f.
    Finding asymptotes is from algebra (and the limit stuff above is just the calculus version of the algebra rules). (here) Where are you stuck in the process?

    Quote Originally Posted by onty5577 View Post
    6. Find the intervals on which f is increasing or decreasing.
    What did you see when you graphed this in your calculator? What did you determine from the First Derivative Test?

    Quote Originally Posted by onty5577 View Post
    7. List the coordinates of any local extrema.
    The extrema are at the zeroes of the first derivative. What did you get?

    Quote Originally Posted by onty5577 View Post
    8. Find the intervals on which f is concave up or concave down.
    What did you see when you graphed this in your calculator? What did you determine from the Second Derivative Test?

    Quote Originally Posted by onty5577 View Post
    9. List the coordinates of any points of inflection.
    The inflection points are at the zeroes of the second derivative. What did you get?

    Please be complete. Thank you!

Bookmarks

Posting Permissions

  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •