Identifying Functions and Their Properties

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-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 a vertical line intersects the graph at more than one point, it is not a function.

Front

What is a relation in mathematics?

Back

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

Front

What does it mean for a mapping to be a function?

Back

A mapping is a function if every input is associated with exactly one output.

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.

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 an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

What is the definition of a domain in a function?

Back

The domain of a function is the set of all possible input values (x-values) for the function.

Front

What is the definition of a range in a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.