Finding Asymptotes

Front

What are asymptotes?

Back

Asymptotes are lines that a graph approaches but never touches. They can be vertical, horizontal, or oblique.

Front

Which asymptote(s) are determined by looking at the denominator?

Back

Vertical asymptotes.

Front

How do you find vertical asymptotes?

Back

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

Front

What is a horizontal asymptote?

Back

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

Front

How do you find horizontal asymptotes for rational functions?

Back

Compare the degrees of the numerator and denominator: If the degree of the numerator is less, y=0; if equal, y= leading coefficient of numerator/leading coefficient of denominator; if greater, no horizontal asymptote.

Front

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

Back

x = -1.

Front

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

Back

y = 2/3.

Front

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

Back

The graph approaches the vertical line but does not cross it, often going to positive or negative infinity.

Front

Can a function have more than one vertical asymptote?

Back

Yes, a function can have multiple vertical asymptotes depending on the factors in the denominator.

Front

What is the significance of horizontal asymptotes in a graph?

Back

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