Attributes/Transformations Test

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

For a rational function, the horizontal asymptote can be found by comparing 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). If the degree of the numerator is greater, there is no horizontal asymptote.

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 the vertical asymptote of a rational function?

Back

To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for x. The values of x that make the denominator zero are the vertical asymptotes.

Front

What does it mean if a function has a horizontal asymptote at y = -5?

Back

It means that as x approaches positive or negative infinity, the value of the function approaches -5.

Front

What does it mean if a function has a vertical asymptote at x = 3?

Back

It means that as x approaches 3 from either the left or the right, the value of the function approaches infinity or negative infinity.

Front

What is the significance of asymptotes in graphing functions?

Back

Asymptotes help to understand the behavior of a function at extreme values and where the function is undefined, guiding the overall shape of the graph.

Front

Can a function have both horizontal and vertical asymptotes?

Back

Yes, a function can have both horizontal and vertical asymptotes, indicating its behavior in both the vertical and horizontal directions.

Front

What is the relationship between the degrees of the numerator and denominator in determining horizontal asymptotes?

Back

The degree of the numerator compared to the degree of the denominator determines the existence and position of horizontal asymptotes.

Front

If a rational function has a degree of 2 in the numerator and 3 in the denominator, what is the horizontal asymptote?

Back

The horizontal asymptote is y = 0, since the degree of the numerator is less than the degree of the denominator.