Question

Which polynomial function is best represented by the graph?

a) f(x)=−(x³ −49x)
b f(x)=x³−49x
c) f(x)=−(x³−49x2)
d) f(x)=−(x³+49x)

Answer 1

The polynomial function that best represents the graph is f(x)=−(x³−49x²)

Step-by-step explanation:

The polynomial function that best represents the given graph is option c) f(x)=−(x³−49x²).

First, let's analyze the graph. It has a negative leading coefficient, indicating a downward curve. The graph starts in the positive region at x = 3 and has a positive slope that is decreasing as x increases. These characteristics match the given option c) f(x)=−(x³−49x²).

In this function, the leading coefficient -1 indicates a downward curve, and the term x³ represents a cubic function. The term -49x² represents a quadratic function that helps to further shape the curve of the graph.