Function or Not?

Front

What is a function?

Back

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

Front

How can you tell if a relation is not a function?

Back

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

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

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

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

Back

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

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 paired with exactly one input, meaning no two different inputs produce the same output.

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.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each input x produces a unique output.

Front

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

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.