Functions, Functions, Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

What is the vertical line test?

Back

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

Front

What does it mean for a relation to not be a function?

Back

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

Front

What is a domain in the context of functions?

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 a range in the context of functions?

Back

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

Front

Can a function have repeated x-values?

Back

Yes, a function can have repeated x-values as long as each x-value corresponds to only one y-value.

Front

What is a mapping in mathematics?

Back

A mapping is a relation that pairs each element of one set with an element of another set.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, 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 {(1, 2), (1, 3)}, where the input 1 is associated with two different outputs.

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.