Identifying Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input.

Front

How can you determine if a mapping is a function?

Back

A mapping is a function if no input is associated with more than one output.

Front

What is the vertical line test?

Back

The vertical line test is 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

Does the mapping {(1,2), (2,3), (1,4)} represent a function?

Back

No, because the input '1' is associated with two different outputs (2 and 4).

Front

Does the mapping {(1,2), (2,3), (3,4)} represent a function?

Back

Yes, because each input is associated with exactly one output.

Front

Does the graph of y = x^2 represent a function?

Back

Yes, because for every x-value, there is exactly one y-value.

Front

Does the graph of y = √x represent a function?

Back

Yes, because for every x-value, there is exactly one y-value.

Front

Does the graph of y = ±√x represent a function?

Back

No, because for some x-values, there are two corresponding y-values (positive and negative).

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3.

Front

What is an example of a non-function?

Back

An example of a non-function is the relation {(1,2), (1,3)}.