QZZ 2.6/2.7 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

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 occur at values of x that make the denominator of a rational function equal to zero, provided that the numerator is not also zero at those points.

Front

What is a hole in a graph?

Back

A hole in a graph occurs at a point where both the numerator and denominator of a rational function are zero, indicating that the function is undefined at that point.

Front

How do you identify the location of a hole in a rational function?

Back

To find the location of a hole, factor both the numerator and denominator of the rational function and identify the common factors. The x-value that makes the common factor zero is the location of the hole.

Front

What is the significance of asymptotes in graphing functions?

Back

Asymptotes help to understand the behavior of a function as it approaches certain values, guiding the sketching of the graph and indicating limits of the function.

Front

Back

The vertical asymptote is x=2, and there is a horizontal asymptote at y=0.

Front

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

Back

As the graph approaches a horizontal asymptote, the y-values of the function get closer to the value of the asymptote but never actually reach it.

Front

Can a function have more than one vertical asymptote?

Back

Yes, a function can have multiple vertical asymptotes, typically occurring at different values of x where the denominator is zero.