input (X) and output (Y)
1 8
2 14
3 ?
4 24
5 28
6 34
What is a function rule that expresses these relationship?
3 goes with 18.
The change in Y alternates between 6 and 4 for each increase of X by one.
You could write the rule as:
Y = 5(X-1)+ 8 = 5X + 3 (X odd)
Y = 5(X-2)+ 14 = 5X + 4 (X even)
west side middle school
To find the function rule that expresses the relationship between the input (X) and the output (Y) in the given data, we need to identify the pattern or relationship between the X and Y values.
Looking at the given data, we can observe that the values of Y are obtained by adding 6 to the corresponding values of X. Let's see:
1 + 6 = 7
2 + 6 = 8
3 + 6 = 9
4 + 6 = 10
5 + 6 = 11
6 + 6 = 12
But the actual values of Y in the given data are different from these calculated values. This means that there is another operation being performed on these calculated values.
Looking closer, we can see that after calculating X + 6, the resulting values are doubled to obtain the actual values of Y in the given data. Let's see:
(1 + 6) x 2 = 14
(2 + 6) x 2 = 16
(3 + 6) x 2 = 18
(4 + 6) x 2 = 20
(5 + 6) x 2 = 22
(6 + 6) x 2 = 24
Therefore, the function rule that expresses the relationship between X and Y in the given data is: Y = (X + 6) x 2.
Using this function rule, we can find the missing value of Y for X=3:
Y = (3 + 6) x 2
Y = 9 x 2
Y = 18
Therefore, the missing value of Y for X=3 is 18.