Asymptote 101

What is an asymptote?

  • An asymptote is a line which a function will follow for ever. The function will get closer and closer to this line but will never cross it.
  • Exponential and rational functions have asymptotes.
  • There are 3 kinds of asymptotes: horizontal, vertical, and slant/oblique.
  • Some functions can have more than one asymptote.
  • A function can never have both a horizontal and slant asymptote! Katniss can totally relate. Are you team Gale or team Peeta? Are you team horizontal or team slant asymptote?

 

Some pictures of Asymptotes: *In all of these pictures the functions are red and the asymptotes are not red.*

Screen Shot 2017-06-16 at 1.41.44 AMScreen Shot 2017-06-16 at 1.42.16 AMScreen Shot 2017-06-16 at 1.45.28 AM

Categorizing Asymptotes:

  • The kinds of asymptotes are horizontal, vertical, and slant/oblique.
  • Horizontal and vertical asymptotes are just what they sound like! Horizontal is parallel to the x-axis and vertical is parallel to the y-axis.
  • A slant/oblique asymptote looks just like a linear function.

 

A Science Example:

Carrying capacity is similar to an asymptote because it is an amount that a population can never surpass. It is also similar because in a lot of cases, the population will fluctuate around this number.

 

A Real Life Example:

You see are really cute and hot guy at school. You are really attracted to him so you follow him around and stalk him. However, you are afraid to talk to him so you just closely observe him.

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