Horizontal and Vertical Asymptotes

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 find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of 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 a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input (x) approaches a certain value, typically where the function is undefined.

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes can be found by setting the denominator of a rational function equal to zero and solving for x.

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 y-value.

Front

What is the significance of the horizontal asymptote y=4?

Back

The horizontal asymptote y=4 indicates that as x approaches positive or negative infinity, the function's output approaches 4.

Front

What does the vertical asymptote x=2 indicate?

Back

The vertical asymptote x=2 indicates that the function approaches infinity or negative infinity as x approaches 2 from either side.

Front

How many vertical asymptotes can a function have?

Back

A function can have multiple vertical asymptotes, depending on the number of values that make the denominator zero.

Front

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

Back

The horizontal asymptote is y = 5/2, since the degrees of the numerator and denominator are equal.

Front

What happens to the graph of a function at a vertical asymptote?

Back

At a vertical asymptote, the graph of the function will approach infinity or negative infinity, creating a break in the graph.