Question

the ordered parts (1,3), (2,9), (3,27), (4,81) and (5,243) represents a function. What is a rule that represents this function

Answer 1

The rule is y = 3^x
This is an exponential

If x = 1, then y = 3^x = 3^1 = 3
If x = 2, then y = 3^x = 3^2 = 3*3 = 9
If x = 3, then y = 3^x = 3^3 = 3*3*3 = 27
If x = 4, then y = 3^x = 3^4 = 3*3*3*3 = 81
If x = 5, then y = 3^x = 3^5 = 3*3*3*3*3 = 243

We can see this a number of ways. One is to graph and notice the points steeply increase as x gets larger. So that implies an exponential growth behavior.

Also notice how jumping from 3 to 9 to 27 and so on has us multiplying by 3. This geometric sequence property further confirms we have an exponential rule.