Understanding 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 vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

Does the set of ordered pairs {(1,2), (2,3), (3,4)} represent a function?

Back

Yes, because each input has exactly one output.

Front

Does the set of ordered pairs {(1,2), (1,3), (2,4)} represent a function?

Back

No, because the input '1' has two different outputs (2 and 3).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Is the relation {(2,3), (3,4), (4,5)} a function?

Back

Yes, it is a function because each input has one output.

Front

Is the relation {(2,3), (2,4), (3,5)} a function?

Back

No, it is not a function because the input '2' has two outputs (3 and 4).

Front

What does it mean for a function to be one-to-one?

Back

A one-to-one function is a function where each output is produced by exactly one input.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = mx + b.