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How to Solve for a Horizontal Asymptote

A mathematician will express a horizontal asymptote by writing "lim (x --> infinity) f(x) = L," or saying, "The limit of function F of X as X goes to infinity is L." This means that the points on the curve of the graphed function f(x) will come nearer and nearer a vertical value L on an x-y graph but will never quite reach that value, even if the line continues to infinity. No matter how close the values come to L, they could always come a little bit closer.

Instructions

- 1
  Write the function you want to analyze. For example, (7x^3 - 3x + 1)/(2x^2 - x + 11).
- 2
  Note the exponent of the first term in the numerator and denominator of your function. An exponent is a superscript number to the right of another number or variable. For example, the exponent of the first term in your numerator is 3 and the exponent of the first term in your denominator is 2.
- 3
  Divide the exponent of the first term in your numerator by the exponent of the first term in your denominator. For example, 3/2 = 1.5.
- 4
  Note that your answer, 1.5, is greater than 1. This function does not have a horizontal asymptote.
- 5
  Write another function you want to analyze. For example, (7x^2 - 3x + 1)/(2x^2 - x + 11).
- 6
  Note the exponent of the first term in the numerator and denominator of your function. For example, the exponent of the first term in your numerator is 2 and the exponent of the first term in your denominator is 2.
- 7
  Divide the exponent of the first term in your numerator by the exponent of the first term in your denominator. For example, 2/2 = 1.
- 8
  Note that your answer, 1, is equal to 1. Divide the coefficient of the first term in your numerator by the coefficient of the first term in your denominator because your answer was equal to 1. The coefficient in a term is any number immediately preceding the variable in that term, so the coefficient of 7x is 7. For example, 7/2 = 3.5. The horizontal asymptote of your function is y = 3.5.
- 9
  Write another function you want to analyze. For example, (7x^2 - 3x + 1)/(2x^3 - x + 11).
- 10
  Note the exponent of the first term in the numerator and denominator of your function. For example, the exponent of the first term in your numerator is 2 and the exponent of the first term in your denominator is 3.
- 11
  Divide the exponent of the first term in your numerator by the exponent of the first term in your denominator. For example, 2/3 = 0.667.
- 12
  Note that your answer, 0.667, is less than 1. The horizontal asymptote of your function is y = 0, or the x-axis.

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