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

Back

The horizontal asymptote is y = 2/4 = 1/2.

Front

What is the significance of vertical asymptotes in a graph?

Back

Vertical asymptotes indicate values of x where the function approaches infinity or negative infinity, showing where the function is undefined.

Front

If a function has two vertical asymptotes, what does that imply?

Back

It implies that the function approaches infinity or negative infinity at two different x-values.

Front

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

Back

The horizontal asymptote is y = 0.

Front

How can you determine the number of vertical asymptotes a function has?

Back

You can determine the number of vertical asymptotes by finding the number of distinct values of x that make the denominator zero.