Domain and Range

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output (y-value) for each input (x-value).

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

If a function has the domain {1, 2, 3}, what could be a possible range?

Back

A possible range could be {4, 5, 6} or any other set of values corresponding to the inputs.

Front

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

Back

A mapping is a function if each input is associated with exactly one output.

Front

Is the set of points {(1,2), (2,3), (1,4)} a function?

Back

No, it is not a function because the input '1' is associated with two different outputs (2 and 4).

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 the range of the function f(x) = x^2 for x in the domain of all real numbers?

Back

The range is [0, ∞) because the output (y-value) is always non-negative.

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.