Please check my answer
The ordered pairs (0,1), (1, 6),(2, 36), (3, 216), and (4, 1,296) represent a function. What is a rule that represents this function?
A y=x^6***
B y=6x
C y=x+6
D y=6x
no one wants to text u dude
you show B and D the same.
Pick the one which is really 6^x
x^6 is not what you want. That is
(0,0),(1,1),(2,64)...
Thank you
To determine the rule that represents the given function, we need to analyze the pattern in the ordered pairs. The general form of a function can be written as y = f(x), where f(x) represents the relationship between x and y.
Looking at the given ordered pairs, we can observe that the y-values are increasing rapidly as the x-values increase. If we try raising the x-values to different exponents, we can find the relationship.
Testing Option A: y = x^6
Let's plug in the x-values and see if they match the given y-values:
For x = 0: y = 0^6 = 0
For x = 1: y = 1^6 = 1
For x = 2: y = 2^6 = 64
For x = 3: y = 3^6 = 729
For x = 4: y = 4^6 = 4096
From the calculation, we can see that the y-values obtained from Option A (y = x^6) do not match the given y-values. Therefore, Option A is not the correct rule.
Now let's test the other options:
B) y = 6x
C) y = x + 6
D) y = 6x
To confirm the correct rule, we can plug in the x-values from the ordered pairs into each of the remaining options:
For Option B:
For x = 0: y = 6(0) = 0
For x = 1: y = 6(1) = 6
For x = 2: y = 6(2) = 12
For x = 3: y = 6(3) = 18
For x = 4: y = 6(4) = 24
The y-values obtained from Option B (y = 6x) also do not match the given y-values. Therefore, Option B is not the correct rule.
For Option C:
For x = 0: y = 0 + 6 = 6
For x = 1: y = 1 + 6 = 7
For x = 2: y = 2 + 6 = 8
For x = 3: y = 3 + 6 = 9
For x = 4: y = 4 + 6 = 10
The y-values obtained from Option C (y = x + 6) also do not match the given y-values. Therefore, Option C is not the correct rule.
Finally, let's test Option D:
For x = 0: y = 6(0) = 0
For x = 1: y = 6(1) = 6
For x = 2: y = 6(2) = 12
For x = 3: y = 6(3) = 18
For x = 4: y = 6(4) = 24
The y-values obtained from Option D (y = 6x) match the given y-values exactly. Therefore, the correct rule that represents the given function is Option D: y = 6x.
It's important to note that in situations like these, testing each option by substituting the given x-values is a systematic approach to identify the correct rule based on the pattern exhibited.