Answer
Part A
The values of B that can make the pairing a function include any other real number apart from the other input variables 2 and 4.
(B, 1), (2, 3), (4, 5)
Input variables = B, 2 and 4
Output variables = 1, 3 and 5
For this relation to be a function,
B = Any other number apart from 2 and 4.
A function table will have the input variable characterized by x and the output variable characterized by f(x)
x | f(x)
B | 1
2 | 3
4 | 5
B = Any other number apart from 2 and 4.
Part B
B can take on any real number value as the input variable in order for this to still be a relation.
Explanation
Restating the question as a statement
The question first asks us to find the value of B in the relations given as (B, 1), (2, 3) (4, 5) that makes this relation a function.
Answer the question
To answer the question, we need to first note what a function is.
A function is a pairing/relation that takes up each value of an input variable and gives a corresponding value of an output variable without the same values of the input variable giving different values of the output variable.
So, basically, a given input term in the pairing cannot have two different output answers.
So, in order for the pairing given [(B, 1), (2, 3), (4, 5)] to be termed a function, the value of B cannot take on the values of the other input variable (2 and 4). So, the values of B that can make the pairing a function is any other real number apart from 2 and 4.
(B, 1), (2, 3), (4, 5)
Input variables = B, 2 and 4
Output variables = 1, 3 and 5
For this relation to be a function,
B = Any other number apart from 2 and 4.
A function table will have the input variable characterized by x and the output variable characterized by f(x)
x | f(x)
B | 1
2 | 3
4 | 5
B = Any other number apart from 2 and 4.
For Part B, any input value for B will make this a relation. A relation doesn't have the strict rules that limit what is termed a function.
So, for this question, B can take on any real number value as the input variable in order for this to still be a relation.
Check the answer
To check the answer, we will just put values in place of B and show that the relation is a function or not.
(B, 1), (2, 3), (4, 5)
If B = 2 or 4, it's not a function
(2, 1), (2, 3), (4, 5) (Not a function)
(4, 1), (2, 3), (4, 5) (Not a function)
But if B = Any other number apart from 2 and 4.
(1, 1), (2, 3), (4, 5) (This is a function)
(10, 1), (2, 3), (4, 5) (this is a function)
This adequately helps us to check our answer.
Explaining your reasoning
Look throught the answer session, All of the explanation required have been provided there.
Hope this Helps!!!
