Chat with our AI personalities
The domain would be (...-2,-1,0,1,2...); the range: (12)
The domain is related to the range depending on the equation or equations given. Without this context, the domain for a Cartegian plane (2 dimensions) is simply R, or all real numbers. With a linear equation (absolute value/ dependent variation) a more useful and specific answer can be given.
y=x^2
Yes. The range can have fewer number of entries.As an extreme case, consider f(x) = 3, where x is a Real number.The domain is all Real numbers - infinitely many of them, while the range is one value: 3.A function can contain one-to-one or many-to-one relationships but one-to-many relationships are not permitted. As a result, the cardinality of the range cannot be bigger than the cardinality of the domain.
The simplest answer is that the domain is all non-negative real numbers and the range is the same. However, it is possible to define the domain as all real numbers and the range as the complex numbers. Or both of them as the set of complex numbers. Or the domain as perfect squares and the range as non-negative perfect cubes. Or domain = {4, pi} and range = {8, pi3/2} Essentially, you can define the domain as you like and the definition of the range will follow or, conversely, define the range and the domain definition will follow,