Characteristics of Functions REVIEW

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

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than the value at the first point.

Front

Identify the decreasing interval for the function: (0, 4), (1, 0) U (1, 4), (-1, 1), (-∞, -1) U (1, ∞)

Back

(-∞, -1) U (1, ∞) is the decreasing interval.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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 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, the asymptote is y=0. If they are equal, divide the leading coefficients.

Front

What does the notation [a, b] signify in interval notation?

Back

The notation [a, b] signifies a closed interval that includes both endpoints a and b.

Front

What does the notation (a, b) signify in interval notation?

Back

The notation (a, b) signifies an open interval that does not include the endpoints a and b.

Front

What is the significance of critical points in a function?

Back

Critical points are where the function's derivative is zero or undefined, indicating potential local maxima, minima, or points of inflection.

Front

What is the difference between increasing and decreasing intervals?

Back

Increasing intervals are where the function's value rises as x increases, while decreasing intervals are where the function's value falls as x increases.