functions domain range

Front

What is the definition of 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 definition of 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

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) is associated with exactly one output (y-value).

Front

What is the vertical line test?

Back

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

Front

What is the horizontal line test?

Back

The horizontal line test is used to determine if a function is one-to-one. If a horizontal line intersects the graph at more than one point, the function is not one-to-one.

Front

Given the relation (1, 2), (1, 3), (2, 4), is this a function?

Back

No, because the x-value 1 has two different y-values (2 and 3).

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each x-value has 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), (2, 4)}.

Front

If the domain of a function is {1, 2, 3}, what is the range if the function outputs are {4, 5, 6}?

Back

The range is {4, 5, 6}.

Front

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

Back

The domain is all real numbers except x = 0.