What happens when the degree of the numerator and denominator are equal?

If the numerator and denominator are of the same degree (n=m), then y = a_n / b_m is a horizontal asymptote of the function. If the degree of the denominator is less than the degree of the numerator, then there are no horizontal asymptotes.

What will be the horizontal asymptote if the degree highest power of the numerator is larger than the degree of the denominator?

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 know if a rational function crosses the horizontal asymptote?

1. Determine what the horizontal asymptote is, e.g. y = a where a is a real number.
2. Look at the equation f(x) = a. If that equation has a solution then the function crosses the asymptote. If it doesn’t have a solution then the function doesn’t.

Why do the leading coefficients of numerator and denominator indicate the horizontal asymptote when the degree of the numerator and denominator are the same?

If the rational function is one in which the degree of the numerator is the same as that of the denominator then it will have a horizontal asymptote. If the degree of the numerator is less than that of the denominator, then the function will have a horizontal asymptote at y=0.

When the degree of the numerator of a rational function exceeds the degree of its denominator by one and if the degree of the denominator is not zero then the function?

When the degree of the numerator is exactly one more than the degree of the denominator, the graph of the rational function will have an oblique asymptote. Another name for an oblique asymptote is a slant asymptote.

What happens if numerator is higher than denominator?

When a fraction has a numerator that is greater than or equal to the denominator, the fraction is an improper fraction. And, finally, a mixed number is a combination of a whole number and a proper fraction.

What are the rules for horizontal asymptotes?

Horizontal Asymptotes Rules

• When n is less than m, the horizontal asymptote is y = 0 or the x-axis.
• When n is equal to m, then the horizontal asymptote is equal to y = a/b.
• When n is greater than m, there is no horizontal asymptote.

Why do some rational functions cross the horizontal asymptote?

Vertical A rational function will have a vertical asymptote where its denominator equals zero. Because of this, graphs can cross a horizontal asymptote. A rational function will have a horizontal asymptote when the degree of the denominator is equal to the degree of the numerator.

How do you tell if a rational function crosses an oblique asymptote?

If there is a slant asymptote, y=mx+b, then set the rational function equal to mx+b and solve for x. If x is a real number, then the line crosses the slant asymptote. Substitute this number into y=mx+b and solve for y. This will give us the point where the rational function crosses the slant asymptote.

When the degree of the numerator is less than the degree of the denominator?

The degree of the numerator is less than the degree of the denominator means that the horizontal asymptote will always be at y = 0. The degree of the numerator is greater than the degree of the denominator means that there is no horizontal asymptote.

When the degree of the numerator is greater than the degree of the denominator?