Question 5 of 10These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?A.x y1 5652 5703 5754 5805 585B.x y1 72 2073 4074 6075 807C.x y1 72 213 634 1895 567D.x y1 3252 4003 4754 5505 625
Question
Question 5 of 10These tables of values represent continuous functions. For which function will the y-values be the greatest for very large values of x?A.x y1 5652 5703 5754 5805 585B.x y1 72 2073 4074 6075 807C.x y1 72 213 634 1895 567D.x y1 3252 4003 4754 5505 625
Solution
To determine which function will have the greatest y-values for very large values of x, we need to look at the rate of change (slope) of each function.
A. The rate of change is 5 (570-565 = 5 when x changes from 1 to 2). B. The rate of change is 135 (207-72 = 135 when x changes from 1 to 2). C. The rate of change is 141 (213-72 = 141 when x changes from 1 to 3, so for each unit change in x, the change in y is 141/2 = 70.5). D. The rate of change is 75 (400-325 = 75 when x changes from 1 to 2).
So, for very large values of x, the function with the greatest rate of change will have the greatest y-values. Therefore, the function B will have the greatest y-values for very large values of x.
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