Function vs Non-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 a non-function?

Back

A non-function is a relation where at least one input (x-value) has more than one output (y-value).

Front

What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What does the horizontal line test determine?

Back

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

Front

Give an example of a function.

Back

An example of a function is y = 2x + 3, where each x-value has a unique y-value.

Front

Give an example of a non-function.

Back

An example of a non-function is the relation defined by the equation x^2 + y^2 = 1, which has two y-values for some x-values.

Front

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

Back

In a function, each x-value must correspond to only one y-value to maintain the definition of a function.

Front

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

Back

In a function, a y-value can correspond to multiple x-values, but each x-value must have only one y-value.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

How can you tell if a graph is a function?

Back

You can tell if a graph is a function by using the vertical line test.