11-10-22 Relations, Functions, Domain and Range (Alg)

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

How can you determine if a relation is a function?

Back

A relation is a function if no x-value is repeated; each input must have a unique output.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for a function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for a function.

Front

What does it mean if a relation is not a function?

Back

It means that at least one input (x-value) is associated with more than one output (y-value).

Front

Provide an example of a relation that is not a function.

Back

{(1,-5), (-1,6), (1,5), (6,-3)} is not a function because the input '1' has two different outputs (-5 and 5).

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function; if a vertical line intersects the curve at more than one point, it is not a function.

Front

What are independent and dependent variables in a function?

Back

The independent variable is the input (x-value), while the dependent variable is the output (y-value) that depends on the input.

Front

What is a one-to-one function?

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.

Front

What is a many-to-one function?

Back

A many-to-one function is a function where multiple inputs can produce the same output.