Key Features of a Function

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 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

What is a y-intercept?

Back

The y-intercept is the point where the graph of a function intersects the y-axis, represented as (0, y).

Front

What is a maximum value of a function?

Back

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

Front

What is a minimum value of a function?

Back

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

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the value of f(x) also increases.

Front

What does it mean for a function to be decreasing?

Back

A function is decreasing on an interval if, as x increases, the value of f(x) decreases.

Front

What is a continuous function?

Back

A continuous function is a function that can be graphed without lifting the pencil from the paper, meaning there are no breaks or holes in the graph.

Front

What is a discontinuous function?

Back

A discontinuous function is a function that has one or more points at which it is not continuous, resulting in breaks or jumps in the graph.