Explain why there does not exist a function whose domain is {-1,0,3} and whose range is {3,4,7,9}. PLEASE EXPLAIN!!
Each number in the domain would have to correspond to one number in the range. There is one number too many in the range.
Thank You :)
domain and range
To show that there does not exist a function whose domain is {-1, 0, 3} and whose range is {3, 4, 7, 9}, we need to examine the definition of a function and determine if it is possible to assign unique values from the range to each element in the domain.
A function is a rule that assigns each element in the domain to a unique element in the range. In this case, the domain consists of three elements {-1, 0, 3}, and the range has four elements {3, 4, 7, 9}.
To determine if a function exists, we need to ensure that each element in the domain is assigned a single unique element in the range. It is impossible to satisfy this condition in this case because there are more elements in the range (four) than in the domain (three).
As a result, there doesn't exist a function that can map elements from the domain {-1, 0, 3} to the range {3, 4, 7, 9} since it violates the basic definition of a function.
Therefore, the explanation lies in the concept of functions and the requirement for each element in the domain to be mapped uniquely to an element in the range.