6-1: Identify Functions

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 if a graph is 'not a function'?

Back

A graph is 'not a function' if there are x-values that correspond to multiple y-values.

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 one corresponding 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 equation x^2 + y^2 = 1, where some x-values correspond to two y-values.

Front

How can you tell if a table represents a function?

Back

A table represents a function if each x-value is unique and does not repeat.

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 relation?

Back

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

Front

What does it mean for a function to be linear?

Back

A linear function is a function that graphs to a straight line, typically represented by the equation y = mx + b.

Front

What is a non-linear function?

Back

A non-linear function is a function that does not graph to a straight line, such as quadratic or exponential functions.