based on the analysis of the given function and the expected behavior of the relationship, the correct graph is c.
The function representing the relationship is f(x) = -0.012
+ 1.03x + 2.46, where x is the amount of fertilizer used in pounds and f(x) is the number of apples produced in bushels. This is a quadratic function, which means it opens upwards or downwards depending on the sign of the leading coefficient.
The leading coefficient here is -0.012, which is negative. Therefore, the parabola represented by the function opens downwards, meaning the number of apples produced initially increases with increasing fertilizer but eventually starts to decrease as too much fertilizer is used.
Based on this information, we can eliminate graphs that clearly contradict the expected behavior:
Graph a: This graph shows a linear relationship, which cannot represent the parabolic behavior described by the function.
Graph d: This graph shows a constantly increasing relationship, which contradicts the expected decrease after using too much fertilizer.
This narrows down the options to graphs b and c:
Graph b: This graph starts increasing but then levels off, not reaching a clear maximum or minimum point.
Graph c: This graph starts increasing, reaches a maximum point, and then starts decreasing, which aligns with the expected behavior of the quadratic function.
Therefore, based on the analysis of the given function and the expected behavior of the relationship, the correct graph is most likely c.
The question probable may be:
A fruit grower determines that the bushels, f(x), of apples produced depending on the pounds, x, of fertilizer used according to the function f(x)= -0.012
+1.03x+2.46