A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

elleblythe

  • one year ago

How did (2,4) become a point in the graph of f(x)=(x^2-4)/(x-2)?

  • This Question is Closed
  1. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Strictly speaking (2,4) is not part of f(x) as defined. f(x)= x+2, for x \(\ne\) 2

  2. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, but "they" did it incorrectly. It this is in a book or question, I would ask the teacher about it... because (2,4) is not part of f(x)

  3. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    *IF this is...

  4. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    |dw:1434548565383:dw| this is the graph my professor drew @phi

  5. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, notice the circle at (2,4) is *open* that is how people show that a point is *not* on the line. at exactly (2,4) there is a "hole" in the line

  6. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now the question is, "why is there a hole?" the answer: if you look at the original definition of f(x) you see you divide by (x-2) when x is exactly 2 that becomes (2-2) = 0 and we do not allow divide by 0 (the quotient is undefined) so we put an open circle at (2,4) to show that point is not on the line.

  7. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @phi oh so was it just a random point? just to show the continuity of the line on the graph?

  8. phi
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    no, not a random point. if you have time , see https://www.khanacademy.org/math/algebra2/polynomial_and_rational/simplifying-rational-expressions/v/simplifying-rational-expressions-introduction

  9. elleblythe
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    @phi thanks for your help!

  10. 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.