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) is associated with more than one output (y-value).

Front

How can you determine if a graph represents a function?

Back

You can use the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does the term 'ordered pair' mean in the context of functions?

Back

An ordered pair is a pair of numbers (x, y) that represents a point on a graph, where 'x' is the input and 'y' is the output.

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). Each x-value must be unique in a function.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, 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 the set of points {(1, 2), (1, 3)}, where the x-value 1 is paired with two different y-values.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph is a function by checking if any vertical line crosses the graph more than once.

Front

If a mapping has the pairs (2, 4), (3, 5), (2, 6), is it a function?

Back

No, it is not a function because the x-value 2 is associated with two different y-values (4 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 (y-value) is paired with exactly one input (x-value), meaning no two different x-values have the same y-value.