LT 1 & 3 (Preview LT 2) 2024

Front

What is a horizontal asymptote?

Back

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

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the asymptote is y=0. If they are equal, the asymptote is y = leading coefficient of numerator / leading coefficient of denominator.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line that the graph of a function approaches as the input approaches a certain value, typically where the function is undefined.

Front

How do you find vertical asymptotes in a rational function?

Back

Vertical asymptotes can be found by setting the denominator of the rational function equal to zero and solving for x.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

How do you determine the domain of a rational function?

Back

To determine the domain of a rational function, identify values of x that make the denominator zero and exclude them from the domain.

Front

Solve by factoring: z^2 - 6z - 27 = 0

Back

z = -3 or z = 9

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.

Front

What does it mean if a function has no horizontal asymptote?

Back

If a function has no horizontal asymptote, it means that as x approaches infinity or negative infinity, the function does not approach a specific y-value.

Front

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

Back

The relationship is crucial: if the degree of the numerator is less than the denominator, the horizontal asymptote is y=0; if they are equal, the asymptote is the ratio of the leading coefficients.