Function Transformations - how do I find the invariant points?

39,822

You're looking for points where $f(x)=x$. Phrased differently, you're looking for points where $(x,x)$ lies on your graph. Rephrased once more, you're looking for intersection with the line $y=x$.

Share:
39,822

Related videos on Youtube

Kat
Author by

Kat

Updated on January 10, 2020

Comments

  • Kat
    Kat over 3 years

    When they give you a picture of a graph (doesn't matter what kind - linear, parabola, inverse, etc.) how do you find the invariant points?

    • epimorphic
      epimorphic almost 8 years
    • Rock
      Rock over 5 years
      I believe the question is how to determine invariant points between a function and it's inverse. If you're looking to algebraically find the point, you just make the two functions equal each other, and then solve for x.
  • Kat
    Kat almost 8 years
    I get what I am looking for but how do I find it?
  • Zach Stone
    Zach Stone almost 8 years
    Draw the line $y=x$, and look for intersection with the given graph.
  • Kat
    Kat almost 8 years
    Is there any way to do it algebraically?
  • Zach Stone
    Zach Stone almost 8 years
    Wait, are you given a picture or equation? If you have the equation, set $f(x)=x$ and try to solve for $x$. I can't be more specific without more details about what $f$ looks like. Sometimes it's possible, sometimes it's not.
  • Kat
    Kat almost 8 years
    It is just a picture of a graph of two porabolas side by side (one is a reflection over the y-intercept) that will eventually intersect but do not in the picture.
  • Zach Stone
    Zach Stone almost 8 years
    If you don't have any equations, then you can't do any algebra.