A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Find domain, range, x and y intercept, Horizontal and vertical asymptote? How do I do it? f(x)=3^x-9

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The domain is all the possible values you can have for x. There is no value for x where we would have "problems" like dividing by 0 or having a negative under the square root. Therefore, the domain of that function is all real numbers or (-infinity, infinity). The range is all the possible values you can have for y. If you solve for x in your equation, you'll have: \[f(x)+9=3^x\] \[x = \log_{3}[f(x)+9] \] Now, what possible values can we have for f(x)? Since a log cannot have 0 or negative numbers on the inside, f(x) > -9. So, the range is (-9, infinity) There are no vertical asymptotes for exponential functions (just kind of a given if you are precalculus). The horizontal asymptote occurs on the y = -9 when we look at range.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    What about the x and y int? On my solution set i have x-int: (2,0) and y-int: (0,-8). How do you get those answers? I understand the other parts.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh whoops. Forgot about the intercepts. To find the x-intercept, let y = 0 to get 0 = 3^x - 9; solve for x to get x = 2, or the point (2, 0). To find the y-intercept, let x = 0 to get f(x) = 3^0 - 9 = 1 - 9 = -8. So, the y-intercept is at the point (0, -8)

  4. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.