Determining 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

What is the definition of domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input).

Front

What is the definition of range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output).

Front

How can you determine if a relation is a function?

Back

A relation is a function if every input has exactly one output. This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

Front

Given the set of ordered pairs (1,2), (2,3), (3,4), (1,5), is this a function?

Back

No, this is not a function because the input '1' is associated with two different outputs (2 and 5).

Front

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

Back

A graph represents a function if for every x-value (input), there is only one corresponding y-value (output).

Front

Identify the function from the following sets: (1,2), (2,3), (3,4), (4,5) and (1,2), (2,3), (1,4).

Back

The first set (1,2), (2,3), (3,4), (4,5) is a function; the second set is not a function because the input '1' has two outputs (2 and 4).

Front

What is an example of a function in real life?

Back

An example of a function in real life is a vending machine: for each button (input), there is one specific item (output) that is dispensed.

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.