8.5G Functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What does it mean for y to be a function of x?

Back

It means that for every value of x, there is exactly one corresponding value of y.

Front

What is the vertical line test?

Back

A method to determine if a curve is a graph of a function. If a vertical line intersects the graph at more than one point, then it is not a function.

Front

What is a mapping in the context of functions?

Back

A mapping is a way to describe how each element of one set (domain) is paired with an element of another set (range).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Can a function have the same output for different inputs?

Back

No, a function cannot have the same output for different inputs; each input must correspond to exactly one output.

Front

What is an example of a function?

Back

f(x) = 2x + 3 is a function because for every x-value, there is one unique y-value.

Front

What is an example of a relation that is not a function?

Back

The relation {(1, 2), (1, 3)} is not a function because the input 1 corresponds to two different outputs.

Front

What does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements.