The ordered pairs (1, 3), (2, 6), (3, 9), (4, 12) and (5, 15) represent a function. What is a rule that represents this function? a: y=x^3

Question

The ordered pairs (1, 3), (2, 6), (3, 9), (4, 12) and (5, 15) represent a function. What is a rule that represents this function? a: y=x^3 b: y= 3^x c: y=3x d: y= x+3

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Answers ( No )

1. Answer: option c: y = 3x

Justification:

All the ordered pairs meet that the second number of the pair equal 3 times the first number of the pair:

Here is the proof:

Pair         first number times 3   second number of the pair

(1, 3)         3 * 1 = 3                         3   => check

(2,6)          2 * 3 = 6                         6   => check

(3,9)          3 * 3 = 9                         9   => check

(4,12)        3 * 4 = 12                      12 => check

(5, 15)       3 * 5 = 15                      15 => check.

So, all the pairs meet the rule y = 3x

2. In case you don’t know your times-3 numbers well enough to recognize the answer right away, you can check the second data point.
.. a. 2^3 = 8 ≠ 6
.. b. 3^2 = 9 ≠ 6
.. c. 3*2 = 6
.. d. 2 +3 = 5 ≠ 6

Only selection C makes sense.