The ordered pairs (1,6), (2,36), (3,216), (4,1296), and (5,7776) represent a function. What is a rule that represents this function?

thats wierd on mine the first ordered pair is (0,1)

Well the the rule is mostly in the y coordinates, they are all powers of 6

6^1=6
6^2=36
6^3=216
6^4=1296

the x coordinates are just increasing by one

based on that information you can write a rule on how it is changing using x and y

so

x+n=6^x=n

since you add the value of n (be it one or two) and whatever number you get you raise 6 to that value.

Thank you

same mine was too ^

To find a rule that represents the function, we need to observe the pattern in the given ordered pairs. Notice that the y-values (the second element in each ordered pair) are increasing exponentially.

Let's analyze the relationship between the x-values and the y-values. We can see that the y-values are obtained by raising the x-values to some power. Specifically, we can observe that each y-value is obtained by raising its corresponding x-value to the power of 6.

So, the rule that represents this function is:

y = x^6

In this rule, x represents the input (the x-value from the ordered pair), and y represents the output (the y-value from the ordered pair). By plugging in any x-value into this equation, we can find the corresponding y-value.