Function Behavior

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What does it mean for a function to be constant?

Back

A function is constant over an interval if it does not change its value for any input within that interval.

Front

How do you determine where a function is increasing?

Back

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

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 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 output at the second point is less than the output at the first point.

Front

What is an interval in mathematics?

Back

An interval is a set of real numbers that contains all numbers between any two numbers in the set.

Front

What is the notation for an open interval?

Back

An open interval is denoted by parentheses, e.g., (a, b), meaning it does not include the endpoints a and b.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted by brackets, e.g., [a, b], meaning it includes the endpoints a and b.

Front

What does the notation U represent in interval notation?

Back

The notation U represents the union of two intervals, meaning it combines all the values from both intervals.

Front

How can you find the maximum or minimum value of a function?

Back

The maximum or minimum value of a function can be found by analyzing its critical points and endpoints on a given interval.