MATH SOLVE

6 months ago

Q:
# The group of points {(0, 1), (0, 5), (2, 6), (3, 3)} is not a function, but the group of points {(1, 4), (2, 7), (3, 1), (5, 7)} is a function. What do you notice about the two groups of points? What do you think it means to be a function?

Accepted Solution

A:

You can use the definition of a function to classify which mapping is a function and which mapping is not a function.The first group is not a function as there are two outputs for 0The second group is a function as there are single output to each input.What is a function?There are two sets of values. When we connect first set's values with other set, it is called mapping one set's value to other set. All type of mappings are called relations.Such relations which are such that each element of the first set(also called input set or domain) is mapped to only one value of the other set(called codomain, and if all values are occupied, then called range or output set), then such relation is called function.So, for a mapping to be function, we need each input to be mapped to only one output.Using above definitionFor group 1, we see that 0 has output 1 and output 5 both. Since for a mapping to be a function, we need each input to have single output, thus, this group doesn't represent a function.For group 2, we see that each input has only one output, thus,this group represents a function.Remember that we assumed that the pair of points were written as (input, output)Thus.The first group is not a function as there are two outputs for 0The second group is a function as there are single output to each input.Learn more about functions here: