Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as the input (x) approaches positive or negative infinity.

Front

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

Back

For a rational function f(x) = P(x)/Q(x), where P and Q are polynomials, the horizontal asymptote can be determined by comparing the degrees of P and Q. If the degree of P is less than Q, the asymptote is y = 0. If they are equal, the asymptote is y = leading coefficient of P / leading coefficient of Q. If the degree of P is greater than Q, there is no horizontal asymptote.

Front

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

Back

y = 0

Front

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

Back

y = 2

Front

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

Back

y = 3/2

Front

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

Back

y = 0

Front

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

Back

y = 0

Front

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

Back

y = 4

Front

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

Back

If a function has no horizontal asymptote, it means that as x approaches positive or negative infinity, the function does not approach a specific finite value.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.