SOLUTION: The ordered pairs (1,81), (2,100), (3,121), (4,144), and (5,169) represent a function. What is a rule that represents this function?

Algebra ->  Functions -> SOLUTION: The ordered pairs (1,81), (2,100), (3,121), (4,144), and (5,169) represent a function. What is a rule that represents this function?      Log On


   

Question 914230: The ordered pairs (1,81), (2,100), (3,121), (4,144), and (5,169) represent a function. What is a rule that represents this function?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
81, 100, 121, 144, 169 are perfect squares

9^2 = 81
10^2 = 100
11^2 = 121
12^2 = 144
13^2 = 169

Notice how we're squaring something each time. The only thing changing is that base (9 to 10 to 11 etc)

So naturally we'd say y=x%5E2 but notice how x = 1 pairs with y = 81. So we can't just say y=x%5E2 because x+=+1 leads to y+=+1

So we have to change the "x" to "x+8" to make sure x = 1 leads to y = 81. We do the +8 to get 1 to 9 (1+8 = 9)

Notice: y=%28x%2B8%29%5E2=%281%2B8%29%5E2+=+9%5E2=81

I'll let you try out the others.

So the function is f%28x%29=%28x%2B8%29%5E2

Let me know if you need more help or if you need me to explain a step in more detail.
Feel free to email me at jim_thompson5910@hotmail.com
or you can visit my website here: http://www.freewebs.com/jimthompson5910/home.html

Thanks,

Jim