Question 1088778
<font color="black" face="times" size="3">
Note how for each (x,y) pair of points given we see that x*y = 60


For instance, the point (4,15) has x = 4 and y = 15 so x*y = 4*15 = 60


Another example: (x,y) = (6,10) means x = 6 and y = 10, so x*y = 6*10 = 60


The fact that this is true for ALL of the points shown indicates we have an inverse variation of the form x*y = k where k = 60 in this case.


Therefore, the answer is <font color=red>B.) An inverse function is the best model because the products of corresponding x- and y-values are equal. </font>


--------------------------------------------------------------------------


Side Notes:


Note1: The term "product" means "result of multiplication". For example, the product of 2 and 5 is 10. In other words, 10 is the product after the result of multiplying 2 and 5.


Note2: Choice A is correct to a certain degree. For any inverse variation, as x increases, y will decrease (and vice versa). We have a sort of "opposites" dynamic going on here. However, this isn't strong enough of a condition. There are other functions that have this property. One such example are linear functions with negative slope. Inverse variation functions are not linear.


Note3: Solve x*y = 60 for y to get y = 60/x, which is the same as f(x) = 60/x. This will graph out a hyperbola with asymptotes as the x and y axis. 
</font>