4.01 - 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

How can you determine if a relation is a function using ordered pairs?

Back

A relation is a function if no x-value is repeated with different y-values in the set of ordered pairs.

Front

What does it mean if an x-value is paired with two different y-values?

Back

It means the relation is not a function.

Front

What is the vertical line test?

Back

A graphical method to determine if a curve is a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

Is the relation {(1,2), (2,3), (3,4)} a function?

Back

Yes, because each x-value has only one corresponding y-value.

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

No, because the x-value 1 is paired with two different y-values (2 and 3).

Front

What is a mapping diagram?

Back

A visual representation of a function that shows how each input is paired with an output.

Front

If a graph passes the vertical line test, what can we conclude?

Back

The graph represents a function.

Front

What is the definition of a domain in a function?

Back

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

Front

What is the definition of a range in a function?

Back

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