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.

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

Back

It means that as x approaches 3, the value of the function increases or decreases without bound (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. The vertical asymptotes indicate where the function is undefined, while horizontal asymptotes indicate the end behavior of the function.

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 horizontal asymptote: if the numerator's degree is less, the asymptote is y = 0; if they are equal, the asymptote is the ratio of leading coefficients.

Front

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

Back

At a vertical asymptote, the graph of the function will approach the asymptote line but will never touch or cross it, resulting in a break in the graph.