Functions: Mapping, Tables, and Points

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

How can you determine if a set of ordered pairs represents a function?

Back

A set of ordered pairs represents a function if no two pairs have the same first element (input) with different second elements (outputs).

Front

What does it mean for a table to represent a function?

Back

A table represents a function if each input value corresponds to exactly one output value.

Front

What is the vertical line test?

Back

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

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represents a point in a coordinate system, where 'x' is the input and 'y' is the output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.

Front

What is the significance of the first element in an ordered pair?

Back

The first element in an ordered pair represents the input value in a function.