Identifying Functions

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

How can you determine if a relation is a function?

Back

A relation is a function if every input (x-value) corresponds to 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 does it mean for a set of ordered pairs to be a function?

Back

For a set of ordered pairs to be a function, no two pairs can have the same first element (x-value) with different second elements (y-values).

Front

Is the set {(1, 2), (2, 3), (1, 4)} a function?

Back

No, it is not a function because the input '1' corresponds to two different outputs (2 and 4).

Front

Is the set {(3, 5), (4, 5), (5, 5)} a function?

Back

Yes, it is a function because each input corresponds to exactly one output.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is related to 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 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.