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 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 does NOT pass the vertical line test?

Back

A graph that has at least one vertical line intersecting it at more than one point.

Front

What must be true for a relation to be a function?

Back

Each x value must have only one corresponding y value.

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 y value.

Front

What is an example of a function?

Back

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

Front

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

Back

The relation defined by the equation x^2 + y^2 = 1 is not a function because a vertical line can intersect it at two points.

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 y value, confirming that the graph represents a function.

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 (x) and an output (y).

Front

What is the difference between a function and a non-function?

Back

A function has one output for each input, while a non-function may have multiple outputs for a single input.