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##### Asked by: Annelies Villoria

science space and astronomy# How do you find an asymptote of a graph?

Last Updated: 25th May, 2020

**graph**will have a vertical

**asymptote**at x=a if the denominator is zero at x=a and the numerator isn'tzero at x=a . If n<m then the x -axis is the horizontal

**asymptote**. Ifn=m then the line y=ab y = a b is thehorizontal

**asymptote**. If n>m there will be no horizontal

**asymptotes**.

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Similarly one may ask, how do you find the horizontal asymptote of a graph?

**Finding Horizontal Asymptotes of RationalFunctions**

- If both polynomials are the same degree, divide thecoefficients of the highest degree terms.
- If the polynomial in the numerator is a lower degree than thedenominator, the x-axis (y = 0) is the horizontal asymptote.

how do you find the asymptotes of an exponential function? Certain **functions**, such as **exponentialfunctions**, always have a horizontal **asymptote**. A**function** of the form f(x) = a (b^{x}) + c always hasa horizontal **asymptote** at y = c. For example, the horizontal**asymptote** of y = 30e^{–}^{6x} –4 is: y = -4, and the horizontal **asymptote** of y = 5(2^{x}) is y = 0.

Besides, how do you find the asymptote of an equation?

Vertical **asymptotes** can be found by solving the**equation** n(x) = 0 where n(x) is the denominator of thefunction ( note: this only applies if the numerator t(x) is notzero for the same x value). The graph has a vertical**asymptote** with the **equation** x = 1.

How do you define Asymptotes?

**Asymptotes**. An **asymptote** of a curve y=f(x)that has an infinite branch is called a line such that the distancebetween the point (x,f(x)) lying on the curve and the lineapproaches zero as the point moves along the branch to infinity.**Asymptotes** can be vertical, oblique (slant) andhorizontal.