Characteristics of Functions

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

Define the domain of a function.

Back

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

Front

Define the range of a function.

Back

The range of a function is the complete set of possible values of the dependent variable (output) that results from using the function.

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 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 at the first point.

Front

What is a constant function?

Back

A constant function is a function that does not change its value; it has the same output for every input.

Front

How do you identify the maximum value of a function?

Back

The maximum value of a function is the highest point on the graph of the function, where the function changes from increasing to decreasing.

Front

How do you identify the minimum value of a function?

Back

The minimum value of a function is the lowest point on the graph of the function, where the function changes from decreasing to increasing.

Front

What is an interval in the context of functions?

Back

An interval is a range of values on the x-axis over which a function is analyzed, often expressed in the form (a, b) or [a, b].

Front

What does it mean for a function to be constant over an interval?

Back

A function is constant over an interval if it takes the same value for every input within that interval.