Graph Functions Flashcard

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

Which graph represents a function?

Back

A graph that passes the vertical line test.

Front

What is a relation in mathematics?

Back

A relation is any set of ordered pairs (x, y). It can include functions, but not all relations are functions.

Front

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

Back

If a graph fails the vertical line test, it means that there are at least two points with the same x-value but different y-values, indicating it is not a function.

Front

Can a vertical line be considered a function?

Back

No, a vertical line is not a function because it fails the vertical line test.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has one output, while a relation can have multiple outputs for a single input.

Front

What is an example of a function?

Back

The equation y = 2x + 3 is a function because for every x-value, there is one corresponding y-value.

Front

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

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 has two different outputs.

Front

What does it mean for a graph to represent both a relation and a function?

Back

If a graph represents both a relation and a function, it means it passes the vertical line test and every x-value corresponds to one y-value.