Functions, Functions, Functions

Front

What is a function in mathematics?

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

How can you determine if a relation is a function?

Back

A relation is a function if every x-value (input) has exactly one corresponding y-value (output).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph is not a function.

Front

What are the domain and range of a function?

Back

The domain is the set of all possible input values (x-values) for a function, while the range is the set of all possible output values (y-values).

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph, characterized by a constant rate of change.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, indicating that the rate of change is not constant.

Front

What is the difference between independent and dependent variables in a function?

Back

The independent variable is the input of the function (usually x), while the dependent variable is the output (usually y) that depends on the input.

Front

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

Back

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

Front

What is a function table?

Back

A function table is a way to organize input-output pairs of a function, showing how each input corresponds to an output.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each element of the domain is paired with an element of the range.