Identifying Functions

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

Back

No, because the x-value 2 has two different y-values (3 and 5).

Front

Which of the following sets of ordered pairs is a function? {(1, 2), (2, 3), (1, 4)} or {(1, 2), (2, 3), (3, 4)}?

Back

{(1, 2), (2, 3), (3, 4)} is a function because each x-value is unique.

Front

What does it mean for a relation to not be a function?

Back

It means that at least one x-value is paired with more than one y-value.

Front

Identify if the following is a function: {(4, 5), (4, 6), (5, 7)}

Back

Not a function, because the x-value 4 has two y-values (5 and 6).

Front

What is the vertical line test?

Back

A method to determine if a relation is a function by checking if a vertical line intersects the graph at more than one point.

Front

If f(x) = 2x + 3, what is f(2)?

Back

f(2) = 2(2) + 3 = 7.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

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.