8.5G Functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs (x-values) and a set of possible outputs (y-values) such that 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

The vertical line test is 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 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

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, but each x-value must correspond to only one y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each x-value, there is a unique y-value.

Front

What is a non-function?

Back

A relation that assigns multiple outputs (y-values) to a single input (x-value) is not a function.

Front

How can you tell if a mapping represents a function?

Back

A mapping represents a function if each x-value corresponds to exactly one y-value.