Which function rule represents the data in the table below?
input (X) 1 2 3 4 5
output (Y) 9 12 15 18 21
A: y=4+5x
B: y=3+6x
C: y=5+4x
D: y=6+3x
C: y=5+4x
To find the function rule that represents the given data, we need to observe the relationship between the input (x) and the output (y).
Looking at the data in the table, we can see that as the input increases by 1, the output increases by 3. This means that the rate of change is 3 for each unit increase in x.
Now let's check the options:
A: y = 4 + 5x
If x is 1, then y would be 4 + 5(1) = 9 (incorrect)
If x is 2, then y would be 4 + 5(2) = 14 (incorrect)
B: y = 3 + 6x
If x is 1, then y would be 3 + 6(1) = 9 (correct)
If x is 2, then y would be 3 + 6(2) = 15 (correct)
C: y = 5 + 4x
If x is 1, then y would be 5 + 4(1) = 9 (incorrect)
If x is 2, then y would be 5 + 4(2) = 13 (incorrect)
D: y = 6 + 3x
If x is 1, then y would be 6 + 3(1) = 9 (incorrect)
If x is 2, then y would be 6 + 3(2) = 12 (incorrect)
Therefore, the function rule that represents the given data is B: y = 3 + 6x.