Function vs 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 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 does it mean for a relation to not be 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

Example of a function: {(2,3), (3,4), (4,5)}. Is this a function?

Back

Yes, this is a function because each input has exactly one output.

Front

Example of a relation: {(1,2), (1,3), (2,4)}. Is this a function?

Back

No, this is not a function because the input 1 has two outputs (2 and 3).

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function by showing how each input is paired with an output.

Front

What does it mean for a function to pass the vertical line test?

Back

If a function passes the vertical line test, it means that for every x-value, there is only one corresponding y-value.

Front

Can a function have repeating x-values?

Back

No, a function cannot have repeating x-values with different y-values. Each x-value must map to only one y-value.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

What is the horizontal line test?

Back

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