Horizontal Asymptotes

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that a graph approaches as x approaches positive or negative infinity.

Front

What does it mean if a function has no horizontal asymptote?

Back

It means that as x approaches positive or negative infinity, the function does not approach a specific y-value.

Front

How do you determine the horizontal asymptote of a rational function?

Back

You compare the degrees of the numerator and denominator. If the degree of the numerator is less than the denominator, the horizontal asymptote is y=0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is the horizontal asymptote of the function f(x) = 3x^2 + 2 / 5x^2 + 1?

Back

y = 3/5, since the degrees of the numerator and denominator are equal.

Front

What is the horizontal asymptote of the function f(x) = 2x^3 + 4 / 3x^2 + 1?

Back

No horizontal asymptote, since the degree of the numerator is greater than the degree of the denominator.

Front

If a function approaches y = 1 as x approaches infinity, what is the horizontal asymptote?

Back

y = 1.

Front

For the function f(x) = 1/x, what is the horizontal asymptote?

Back

y = 0, as x approaches positive or negative infinity.

Front

What are the horizontal asymptotes of the function f(x) = (2x^2 + 3)/(4x^2 + 5)?

Back

y = 1/2, since the degrees of the numerator and denominator are equal.

Front

What happens to the horizontal asymptote if the degree of the numerator is less than the degree of the denominator?

Back

The horizontal asymptote is y = 0.

Front

What is the horizontal asymptote of the function f(x) = 5x + 2 / 2x^2 - 3?

Back

y = 0, since the degree of the numerator is less than the degree of the denominator.