Question 79979
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Is the relationship between the varibles in the table a direct variation, 
an inverse or neither? If it is a direct inverse write a function to model
it. 
X=  -2 3  5  6 
Y= -11 4 13 32 

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If it is a direct variation, then if we substitute all of them 
in the equation

Y = kK

the value of k will be the same.

-11 = k(-2)
-11 = -2k
{{{(-ll)/(-2)}}} = k
{{{11/2}}} = k

4 = k(3)
4 = 2k
{{{4/2}}} = k
{{{2}}} = k

So it can't be a direct variation because those two values
of k are not the same.  But we might as well
see what the other values of k are:

13 = k(5)
13 = 5k
{{{(l3)/5}}} = k

{{{(32)/(6)}}} = k
{{{16/3}}} = k

They certainly aren't all the same, so this is not a direct variation.

If it is an inverse variation, then if we substitute all of them in the
equation

Y = {{{k/X}}}

the value of k will be the same.

-11 = {{{k/(-2)}}}
 22 =  k

4 = {{{k/3}}}
12 = k

So it can't be an inverse variation either because those
values of k are not the same.  But we might as well
see what the other values of k are:

13 = {{{k/5}}}
65 = k

32 = {{{k/6}}}
192 = k

They certainly aren't all the same!  So it's not an inverse
variation either.  So it's NEITHER!

However, the data fits the formula:
 
     Y = {{{(97X^3-546X^2+371X+1854)/168}}}

Edwin</pre>