how to find asymptotes of a rational function

Finding Horizontal Asymptotes of Rational Functions

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

1. How do you find asymptotes of a function?
2. What are the rules for vertical asymptotes?
3. How do you find the vertical and horizontal asymptotes of a graph?
4. What is the horizontal asymptote?
5. How do you find the horizontal asymptote?
6. What is the rule for horizontal asymptote?
7. How do you find the asymptotes of a graph?

How do you find asymptotes of a function?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

1. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
2. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.

What are the rules for vertical asymptotes?

To determine the vertical asymptotes of a rational function, all you need to do is to set the denominator equal to zero and solve. Vertical asymptotes occur where the denominator is zero. Remember, division by zero is a no-no. Because you can't have division by zero, the resultant graph thus avoids those areas.

How do you find the vertical and horizontal asymptotes of a graph?

The vertical asymptotes will occur at those values of x for which the denominator is equal to zero: x2 − 4=0 x2 = 4 x = ±2 Thus, the graph will have vertical asymptotes at x = 2 and x = −2. To find the horizontal asymptote, we note that the degree of the numerator is one and the degree of the denominator is two.

What is the horizontal asymptote?

Horizontal asymptotes are horizontal lines the graph approaches. ... 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.

How do you find the horizontal asymptote?

The horizontal asymptote of a rational function can be determined by looking at the degrees of the numerator and denominator.

1. Degree of numerator is less than degree of denominator: horizontal asymptote at y = 0.
2. Degree of numerator is greater than degree of denominator by one: no horizontal asymptote; slant asymptote.

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.

How do you find the asymptotes of a graph?

An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.