# What is the equation for the horizontal asymptote?

Category:
science
space and astronomy

A function of the form f(x) = a (b

^{x}) + c always has a**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.

Likewise, how do you find the equation of the horizontal asymptote?

**To find horizontal asymptotes:**

- If the degree (the largest exponent) of the denominator is bigger than the degree of the numerator, the horizontal asymptote is the x-axis (y = 0).
- If the degree of the numerator is bigger than the denominator, there is no horizontal asymptote.

**vertical asymptotes**will occur at those values of x for which the denominator is equal to zero: x − 1=0 x = 1 Thus, the graph will have a

**vertical asymptote**at x = 1. To find the

**horizontal asymptote**, we note that the degree of the numerator is two and the degree of the denominator is one.

Then, what is the rule for horizontal asymptote?

The three **rules** that **horizontal asymptotes** follow are based on the degree of the numerator, n, and the degree of the denominator, m. If n < m, the **horizontal asymptote** is y = 0. If n = m, the **horizontal asymptote** is y = a/b. If n > m, there is no **horizontal asymptote**.

A function of the form f(x) = a (b^{x}) + c always has a **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.