Function Features

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for a function to be increasing?

Back

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

Front

What does it mean for a function to be decreasing?

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

What is an interval in mathematics?

Back

An interval is a range of numbers between two endpoints, which can be open (not including endpoints) or closed (including endpoints).

Front

How do you denote an increasing interval?

Back

An increasing interval is denoted using parentheses or brackets, such as (a, b) or [a, b], where the function increases from point a to point b.

Front

What is a local minimum?

Back

A local minimum is a point on the graph of a function where the function value is lower than all nearby points.

Front

What is a local maximum?

Back

A local maximum is a point on the graph of a function where the function value is higher than all nearby points.

Front

What is the significance of the derivative in determining increasing or decreasing intervals?

Back

The derivative of a function indicates the slope of the function. If the derivative is positive, the function is increasing; if negative, the function is decreasing.

Front

What is the notation for a decreasing interval?

Back

A decreasing interval is denoted similarly to an increasing interval, such as (a, b) or [a, b], where the function decreases from point a to point b.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.