Apr 19 - Functions, Domain, Range, Intervals, Max/Min

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

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

How do you express the domain in interval notation?

Back

The domain is expressed in interval notation by using brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints.

Front

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

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What does it mean for a function to have a maximum point?

Back

A maximum point is the highest point on the graph of a function within a given interval.

Front

What does it mean for a function to have a minimum point?

Back

A minimum point is the lowest point on the graph of a function within a given interval.

Front

How do you determine the intervals of increase and decrease for a function?

Back

To determine intervals of increase and decrease, analyze the first derivative of the function.

Front

What is the difference between open and closed intervals?

Back

An open interval does not include its endpoints, while a closed interval includes its endpoints.

Front

What is the notation for the domain of a function that is defined for all real numbers?

Back

The notation for the domain of a function defined for all real numbers is (-∞, ∞).