vertical and horizontal asymptotes

Front

What is an asymptote?

Back

An asymptote is a line that a graph approaches but never touches or crosses. It can be vertical, horizontal, or oblique.

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.

Front

What is a horizontal asymptote?

Back

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

Front

How do you find vertical asymptotes algebraically?

Back

Set the denominator of a rational function to zero and solve for x.

Front

How do you find horizontal asymptotes for rational functions?

Back

1. If the degree of the numerator is less than the degree of the denominator, y = 0. 2. If the degrees are equal, y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is the significance of vertical asymptotes in a graph?

Back

Vertical asymptotes indicate values of x where the function is undefined and the graph will approach infinity.

Front

What is the significance of horizontal asymptotes in a graph?

Back

Horizontal asymptotes indicate the behavior of the function as x approaches infinity or negative infinity.

Front

Example of a function with a vertical asymptote: f(x) = 1/(x-2). What is the vertical asymptote?

Back

x = 2.

Front

Example of a function with a horizontal asymptote: f(x) = 3x/(2x+1). What is the horizontal asymptote?

Back

y = 3/2.

Front

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

Back

The graph will rise or fall towards infinity as it approaches the vertical asymptote.