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f(n)=something

Baffled, the chief of police broadcast a special TV report asking the citizens to be on the lookout for the Phantom Number Cruncher:"Citizens of Gallatin: If anyone has any information that can help us catch the Phantom Number Cruncher, please call the number on your screen." The phone number "354-8217" flashed on the screen. No sooner did the numbers appear on the screen when the numbers flickered and reappeared as "7 13 10 - 22 4 1 19." Moments later, static distorted the TV picture, and replacing the chief of police was none other than the Phantom himself!The Phantom was a sight to behold, with his shock of green hair and wacky number mask. He leaned forward and sneered, "Oh yes, dear citizens! I've taken all your numbers and changed them with my special Presto Function Changer!" At this, he tossed back his head and let loose a crazy, high-pitched laugh."You poor, pathetic numerical nincompoops," he continued. "The only way you'll get your numbers back is if you can figure out the FUNCTIONS that changed them!" Static filled the screen, and we were returned to the exasperated police chief."We will get our numbers back, I promise!" thundered the chief. "Math Maven, if you and your talented mathematics detectives are watching this broadcast, on behalf of the town of Gallatin, we need you! Help us get our numbers back and put the Phantom Number Cruncher in his place!"Help the police chief crack the code of that Presto Function Changer. Find the FUNCTION the Phantom is using to change the town's numbers. Put your answer in the form f(n) = something
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1 Answer

You could first try a linear relationship, with two of the points being (3, 7) and (5, 13).

slope = m = (13-7)/(5-3) = 6/2 = 3

You could use point slope formula with the point (3, 7):

y - 7 = 3(x - 3)

y - 7 = 3x - 9

y = 3x - 2, and then change the y to f(n) and the x to n.


f(n) = 3n-2
 
f(3) = 3(3) - 2 = 7
 
f(5) = 3(5) - 2 = 13
 
f(4) = 3(4) - 2 = 10
 
f(8) = 3(8) - 2 = 22
 
f(2) = 3(2) - 2 = 4
 
f(1) = 3(1) - 2 = 1
 
f(7) = 3(7) - 2 = 19
 
 
 
Hope this helps you.
 
Regards,
Jason