The ordered pairs (1,1) (2,16) (3, 81) (4, 256) and (5, 625) represent a function. What is a rule that represents this function? (1 point)
1. y = 4^x
2. y = 4 x
3. y = x^4
4. y = x + 4
The correct rule that represents this function is:
3. y = x^4
To find the rule that represents the function, we need to examine the pattern in the ordered pairs.
Looking at the values of x and y, we can observe that the y-values are obtained by raising the x-values to the power of 4.
Therefore, the correct choice for the rule that represents the function is:
3. y = x^4
To find the rule that represents the given function, we need to analyze the pattern between the x and y values. Let's look at the x and y values of the given ordered pairs:
(1, 1)
(2, 16)
(3, 81)
(4, 256)
(5, 625)
By observing the pattern, we can see that the y-values are obtained by raising the x-values to some power. In other words, the y-value is equal to the x-value raised to a certain exponent.
If we test the given options, we find that option 3, y = x^4, correctly represents the given function.
For example:
When x = 1, (1^4) = 1, which matches the y-value of 1.
When x = 2, (2^4) = 16, which matches the y-value of 16.
When x = 3, (3^4) = 81, which matches the y-value of 81.
And so on, the pattern follows for all the ordered pairs.
Therefore, the correct rule that represents the given function is y = x^4 (Option 3).