Relations & Functions, discrete continuous, one to one

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 is a one-to-one function?

Back

A one-to-one function is a function where each output (y-value) is paired with exactly one input (x-value). No two different inputs can produce the same 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 is a discrete function?

Back

A discrete function is a function that has distinct, separate values. It is often represented by a set of points.

Front

What is a continuous function?

Back

A continuous function is a function that has no breaks, jumps, or holes in its graph. It can take any value within a given range.

Front

Which of the following is not a function? {(0,1), (1,2), (2,3), (3,4)}, {(0,2), (1,3), (4,3), (1,2)}, {(1,3), (4,2), (2,0), (3,4)}, {(1,2), (2,2), (3,2), (4,2)}

Back

{(0,2), (1,3), (4,3), (1,2)} is not a function because the input '1' has two different outputs.

Front

What is the difference between a relation and a function?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input has exactly one output.

Front

What does it mean for a function to be onto?

Back

A function is onto if every element in the range is mapped to by at least one element in the domain.