Domain, Range, Increasing, Decreasing, End Behavior

Front

What is the definition of domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that the function can produce.

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 value at the second point is greater than the function 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 value at the second point is less than the function value at the first point.

Front

What is end behavior in the context of functions?

Back

End behavior describes the behavior of a function as the input values approach positive or negative infinity.

Front

How do you determine the domain of a function from its graph?

Back

The domain can be determined by identifying all the x-values for which the graph has points.

Front

How do you determine the range of a function from its graph?

Back

The range can be determined by identifying all the y-values that the graph reaches.

Front

What is the notation for an open interval?

Back

An open interval is denoted by parentheses, e.g., (a, b), meaning that a and b are not included in the interval.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted by brackets, e.g., [a, b], meaning that a and b are included in the interval.

Front

What is the difference between increasing and decreasing intervals?

Back

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