Functions

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

Which of the following is a function? (6,-5) (7,-3) (8,-1) (9,1) or (5,9) (5,-7)?

Back

(6,-5) (7,-3) (8,-1) (9,1) is a function because each x-value is unique.

Front

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

Back

A relation is not a function if at least one x-value is paired with more than one y-value.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if it passes the vertical line test; no vertical line intersects the graph at more than one point.

Front

What is the vertical line test?

Back

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

Front

Is the relation {(1,2), (2,3), (1,4)} a function? Why or why not?

Back

No, because the x-value 1 is paired with two different y-values (2 and 4).

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 a 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 a function.

Front

If a function has the ordered pairs (2,3), (3,4), (4,5), what is the output when the input is 3?

Back

The output is 4.

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.