Question

A complete graph of the polynomial function f is provided. Use your knowledge of the domain, range, behavior at each x intercept, end behavior, symmetry, local and global extreme values, and intervals of increasing and decreasing to select the best choice of the polynomial function, f.

Answer 1

The graph represents a polynomial graph, and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

How to determine the equation?

From the graph, we have the following observations:

• The graph has a turning point at x = 2
• The graph changes the factor of its direction at x = -5

This means that the graph has a multiplicity of 2 at x = 2 and a multiplicity of 3 at x = -5

So, we have:

f(x) = a(x + 5)³(x - 2)²

The curve is inverted,

This means that a < 0

Assume a = -1.

Then, we have:

f(x) = -(x + 5)³(x - 2)²

Hence, the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²

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