Is it a Function?

Front

What is a function?

Back

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

Front

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

Back

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

Front

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

Back

Yes, because each x-value has only one y-value paired with it.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a relation is a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

If a relation has the pairs (2, 5), (2, 6), (3, 7), is it a function?

Back

No, because the x-value 2 has two different y-values (5 and 6).

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 output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

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.

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

Is the relation {(1, 2), (3, 4), (5, 6)} a function?

Back

Yes, because each x-value has only one y-value paired with it.