Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once. This is known as the Vertical Line Test.

Front

What is the domain of a function?

Back

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

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

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if at least one input (x-value) is associated with more than one output (y-value).

Front

Example of a function: (1, 2), (2, 3), (3, 4). Is this a function?

Back

Yes, this is a function because each x-value is paired with exactly one y-value.

Front

Example of a relation that is not a function: (1, 2), (1, 3). Is this a function?

Back

No, this is not a function because the x-value '1' is paired with two different y-values (2 and 3).

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with its corresponding output.

Front

What is a one-to-one function?

Back

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

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, typically in the form y = mx + b, where m is the slope and b is the y-intercept.