Function or Not a Function

Front

What is a function?

Back

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

Front

What is the definition of 'not a function'?

Back

A relation is not a function if at least one input (x-value) has more than one output (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

What is the horizontal line test?

Back

The horizontal line test checks if a function is one-to-one. If a horizontal line intersects the graph more than once, the function is not one-to-one.

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 corresponding y-value.

Front

What does it mean if a relation has repeated x-values?

Back

If a relation has repeated x-values with different y-values, it is not a function.

Front

What is an example of a function?

Back

An example of a function is the relation {(1, 2), (2, 3), (3, 4)} where each x-value has a unique y-value.

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), (2, 4)} because the x-value 1 has two different y-values.

Front

How can you tell if a table represents a function?

Back

A table represents a function if no x-value is repeated with different y-values.

Front

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

Back

The x-value is the input of the function, and it must be unique for each output (y-value).