We want to determine if the input and output pairings represent a function, a linear function.
We can inspect the pattern for x and y.
Let me predict a relationship of the form y = ax + b.
Let's check if it's correct, by trying a pair to generate the equation, then check if it works for the others.
I select the pair, 4 and 11.
If I put it in the equation, I get;
11= 4a+b.
Let me try another pair, 5 and 13
I obtain, 13 = 5a + b
I have 2 equations now.
13=5a + b
11= 4a + b
Subtract equation ii from i to obtain
2=a.
Put a =2 back in equation I to obtain;
13=5(2)+b
13= 10 + b , 13 - 10 = b , b =3.
Therefore, the pairing is a function,
The rule of the function is, multiply by 2 and add 3.
That is option B
