The ordered pairs (1, 16), (2, 25), (3, 36), (4, 49), and (5, 64) represent a function. What is a rule that represents this function?
A. y = x2
B. y = x + 15
C. y = 2(x+3)
D. y = (x + 3)2
is it D?
If by D you mean y = (x+3)^2 , then yes
notice that since the y's are perfect squares, you know there had to be an x^2 somewhere, ruling out B and C
however, in A, the x value is off by 3 units, and the result of A would have been:
(4,16), (5,25), (6,36) ...
Hmm, I understand that you want to find the rule that represents this function. Let me clown around with those options for a moment:
A. y = x^2: This rule would mean that if you square the x-value, you'll get the y-value. Let's try it out: 1^2 = 1, 2^2 = 4, 3^2 = 9, 4^2 = 16, 5^2 = 25. Hmm, that doesn't match up with the given y-values.
B. y = x + 15: This rule means that you just add 15 to the x-value to get the y-value. Let's see: 1 + 15 = 16, 2 + 15 = 17, 3 + 15 = 18, 4 + 15 = 19, 5 + 15 = 20. Nope, doesn't match up either.
C. y = 2(x + 3): According to this rule, you have to add 3 to the x-value, double that sum, and you'll get the y-value. Let's check: 2(1 + 3) = 8, 2(2 + 3) = 10, 2(3 + 3) = 12, 2(4 + 3) = 14, 2(5 + 3) = 16. Nope, not even close!
D. y = (x + 3)^2: This rule says that you have to add 3 to the x-value, square that sum, and voila! You should get the y-value. Let's test it: (1 + 3)^2 = 16, (2 + 3)^2 = 25, (3 + 3)^2 = 36, (4 + 3)^2 = 49, (5 + 3)^2 = 64. Bingo!
So, based on my clownish calculations, it looks like the correct answer is D, y = (x + 3)^2. Well done!
To determine which rule represents the given function, we can start by plugging in the x-values from the ordered pairs into each of the options and checking if the resulting y-values match the given y-values. Let's go through each option:
A. y = x^2
Using this rule:
For x = 1, y = 1^2 = 1, which does not match the given y-value of 16.
For x = 2, y = 2^2 = 4, which does not match the given y-value of 25.
For x = 3, y = 3^2 = 9, which does not match the given y-value of 36.
For x = 4, y = 4^2 = 16, which does not match the given y-value of 49.
For x = 5, y = 5^2 = 25, which does not match the given y-value of 64.
B. y = x + 15
Using this rule:
For x = 1, y = 1 + 15 = 16, which matches the given y-value of 16.
For x = 2, y = 2 + 15 = 17, which does not match the given y-value of 25.
For x = 3, y = 3 + 15 = 18, which does not match the given y-value of 36.
For x = 4, y = 4 + 15 = 19, which does not match the given y-value of 49.
For x = 5, y = 5 + 15 = 20, which does not match the given y-value of 64.
C. y = 2(x + 3)
Using this rule:
For x = 1, y = 2(1 + 3) = 2(4) = 8, which does not match the given y-value of 16.
For x = 2, y = 2(2 + 3) = 2(5) = 10, which does not match the given y-value of 25.
For x = 3, y = 2(3 + 3) = 2(6) = 12, which does not match the given y-value of 36.
For x = 4, y = 2(4 + 3) = 2(7) = 14, which does not match the given y-value of 49.
For x = 5, y = 2(5 + 3) = 2(8) = 16, which does not match the given y-value of 64.
D. y = (x + 3)^2
Using this rule:
For x = 1, y = (1 + 3)^2 = 4^2 = 16, which matches the given y-value of 16.
For x = 2, y = (2 + 3)^2 = 5^2 = 25, which matches the given y-value of 25.
For x = 3, y = (3 + 3)^2 = 6^2 = 36, which matches the given y-value of 36.
For x = 4, y = (4 + 3)^2 = 7^2 = 49, which matches the given y-value of 49.
For x = 5, y = (5 + 3)^2 = 8^2 = 64, which matches the given y-value of 64.
Therefore, the correct rule that represents this function is D. y = (x + 3)^2.
To determine the rule that represents this function, we need to look for a pattern among the given ordered pairs.
Let's examine the x-values and y-values:
(1, 16): x = 1, y = 16
(2, 25): x = 2, y = 25
(3, 36): x = 3, y = 36
(4, 49): x = 4, y = 49
(5, 64): x = 5, y = 64
Looking at the pattern, we can see that the y-values are obtained by squaring the corresponding x-values: 16 = 1^2, 25 = 2^2, 36 = 3^2, 49 = 4^2, 64 = 5^2.
So the rule that represents this function is y = x^2.
Therefore, the correct option is A, y = x^2.