Relations and 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 relation is not a function?

Back

A relation is not a function if at least one input is associated with more than one output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, as long as each input has only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each input x has a unique output.

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 y = ±√x, where each positive x-value has two corresponding y-values.

Front

What is the definition of a relation?

Back

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

Front

How can you determine if a set of ordered pairs represents a function?

Back

You can determine if a set of ordered pairs represents a function by checking if any input value is repeated with different output values.

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 one-to-one?

Back

A one-to-one function is a function where each output is associated with exactly one input, meaning no two different inputs produce the same output.