Domain/Range/Function/Not Function

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value in the domain, there is one and only one corresponding y-value in the 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) that the function can accept.

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 is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each input x, there is 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)}, because the input 1 corresponds to two different outputs.

Front

What does the vertical line test determine?

Back

The vertical line test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph is not a function.

Front

What is the output of the function f(x) = x^2 for x = 3?

Back

The output is 9, since f(3) = 3^2 = 9.

Front

What is the input of the function f(x) = 2x + 1 when the output is 5?

Back

The input is 2, since 5 = 2(2) + 1.

Front

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

Back

The domain is all real numbers except x = 0, since division by zero is undefined.