Functions and Domain and Range

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every input value (x), there is one and only one output value (y).

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

How can you determine if a relation is a function?

Back

A relation is a function if no two ordered pairs have the same first element (x-value). If any x-value is repeated with different y-values, it is not a function.

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. In other words, each output is produced by exactly one input.

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 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)}, because the input 1 corresponds to two different outputs.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain of f(x) = 1/x is all real numbers except x = 0, since division by zero is undefined.

Front

What is the range of the function f(x) = x^2?

Back

The range of f(x) = x^2 is all real numbers greater than or equal to 0, since the output of a square is always non-negative.

Front

How do you find the domain of a function given a graph?

Back

To find the domain from a graph, identify the x-values for which the graph has points. The domain includes all x-values where the graph exists.