Question

which function rule represents the data in the table below? input (x) 1,2,3,4,5 output (y) 9,14,19,24,29

Answer 1

Term n = a + (n-1) d is the formula for an "arithmetic series (try Google :)
if
a = 4 and d = 5

T1 = 4 + 0 = 4
T2 = 4 + 5 = 9
T3 = 4 + 10 = 14
T3 = 4 + 15 = 19 etc
so this is an arithmetic series with x = n-1

Answer 2

To find the function rule, we can observe that the output (y) increases by 5 for each increase in the input (x). We also notice that when the input is 1, the output is 9.

Therefore, the function rule that represents the data in the table is:
y = 5x + 4

To verify this:
- If x=1, y = 5(1) + 4 = 9
- If x=2, y = 5(2) + 4 = 14
- If x=3, y = 5(3) + 4 = 19
- If x=4, y = 5(4) + 4 = 24
- If x=5, y = 5(5) + 4 = 29