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 set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two different pairs have the same first element (input).

Front

Given the set {(–4, 3), (5, –9), (11, 4), (9, 6), (5, –3), (8, –9), (1, 4)}, is this a function?

Back

No, because the input '5' is associated with two different outputs: -9 and -3.

Front

Given the set {(15, –3), (–6, 9), (–3, 0), (–1, 16)}, is this a function?

Back

Yes, each input is associated with exactly one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x gives a unique output.

Front

What is a non-function?

Back

A non-function is a relation where at least one input is associated with multiple outputs.

Front

What does the vertical line test determine?

Back

The vertical line test determines 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 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.

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.