Classwork on Function, Domain and Range

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 graph represents a function?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does it mean if a relation is not a function?

Back

It means that at least one input (x-value) is associated with more than one output (y-value).

Front

What is the vertical line test?

Back

A method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because each x-value has one corresponding y-value.

Front

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

Back

The relation defined by the equation x^2 + y^2 = 1 is not a function because for some x-values, there are two corresponding y-values.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.