Identifying Functions

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 domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How can you determine if a relation is a function using the vertical line test?

Back

If a vertical line intersects the graph of the relation at more than one point, it is not a function.

Front

What does it mean for x-values to repeat in a relation?

Back

If x-values repeat, it means that there are multiple outputs (y-values) for the same input (x-value), which disqualifies it as a function.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x, there is exactly one y.

Front

What is an example of a non-function?

Back

The relation {(1, 2), (1, 3)} is not a function because the x-value 1 has two different y-values.

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 graphs to a straight line, typically in the form y = mx + b.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form y = ax^2 + bx + c, where a, b, and c are constants.