Asymptotes

Front

What is an asymptote?

Back

A line that a curve approaches, as it heads towards infinity.

Front

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

Back

y = 1/2

Front

What are the vertical asymptotes of the function f(x) = 1 / (x - 2)?

Back

x = 2

Front

How do you find horizontal asymptotes?

Back

Look at the degree of the top and bottom of the function.

Front

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

Back

y = 2/3

Front

What are the asymptotes of the function f(x) = (x + 1) / (x - 2)?

Back

x = 2 and y = 1.

Front

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

Back

x = 1.

Front

What happens to the graph of a function as it approaches its horizontal asymptote?

Back

The graph gets closer to the horizontal line but never touches it.

Front

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

Back

y = 0

Front

What is the definition of a vertical asymptote?

Back

A vertical line that a graph approaches but never touches, typically where the function is undefined.