Functions, Functions, Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

What are the inputs of a function called?

Back

The inputs of a function are called the domain.

Front

What are the outputs of a function called?

Back

The outputs of a function are called the range.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What is the standard form of a linear function?

Back

The standard form of a linear function is Ax + By = C, where A, B, and C are constants.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if each output is produced by exactly one input, meaning no two different inputs produce the same output.

Front

What is a vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function by checking if any vertical line intersects the graph more than once.

Front

What is a piecewise function?

Back

A piecewise function is a function defined by multiple sub-functions, each applying to a certain interval of the domain.