Function or Not a Function

Front

What is a function?

Back

A relation where each input (x value) has exactly one output (y value).

Front

What is the vertical line test?

Back

A method to determine 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 does it mean for a relation to not be a function?

Back

A relation where at least one input (x value) is associated with more than one output (y value).

Front

What is the definition of a domain in a function?

Back

The set of all possible input values (x values) for a function.

Front

What is the definition of a range in a function?

Back

The set of all possible output values (y values) for a function.

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, as long as each x value has only one y value.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because each x value corresponds to exactly one y value.

Front

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

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 corresponds to two different outputs.

Front

What does it mean for a graph to pass the vertical line test?

Back

It means that any vertical line drawn on the graph intersects it at most once, indicating it is a function.

Front

What is the significance of the x-axis in a function?

Back

The x-axis represents the input values (domain) of the function.