Identifying Functions

Front

What is a function?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) where each input is related to exactly one output.

Front

How can you tell if a table represents a function?

Back

A table represents a function if each x-value is paired with only one y-value.

Front

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

Back

A graph is a function if any vertical line drawn through the graph intersects it at most once.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function by checking if a vertical line crosses the graph more than once.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, but each x-value must have only one corresponding y-value.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x-value has a unique y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is the set of points {(1, 2), (1, 3)}, where the x-value 1 is paired with two different y-values.

Front

What does the term 'domain' refer to in functions?

Back

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

Front

What does the term 'range' refer to in functions?

Back

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

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each x-value is paired with a unique y-value, and each y-value corresponds to a unique x-value.