Identify Functions

Front

What is a function?

Back

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

Front

What does it mean for a relation to be a function?

Back

A relation is a function if no 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

Does the following table represent a function? (Example: x: 1, 2, 3; y: 4, 5, 6)

Back

Yes, because each x-value has a unique y-value.

Front

Is the set of ordered pairs {(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

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where each x-value gives a unique y-value.

Front

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

Back

An example is the relation {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

Front

How can you tell if a graph is a function?

Back

You can tell if a graph is a function by using the vertical line test.

Front

What does it mean if a graph passes the vertical line test?

Back

It means that for every x-value, there is only one corresponding y-value, indicating it is a function.

Front

What is the significance of the x-value in a function?

Back

The x-value is the input of the function, and it determines the corresponding y-value (output).