Functions and One to One functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

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

Is the mapping {(1,2), (2,3), (3,4)} a function?

Back

Yes, it is a function because each input has a unique output.

Front

Is the mapping {(1,2), (1,3), (2,4)} a function?

Back

No, it is not a function because the input '1' has two different outputs.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Given the function {(0,1), (1,-3), (2,-4)}, what is the domain?

Back

The domain is {0, 1, 2}.

Front

Given the function {(0,1), (1,-3), (2,-4)}, what is the range?

Back

The range is {1, -3, -4}.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a graph represents a function; if any vertical line intersects the graph more than once, it is not a function.

Front

What does it mean for a function to be onto?

Back

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