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.
1 answer:
The graph represents a polynomial graph , and the equation of the polynomial graph is f(x) = -(x + 5)³(x - 2)²
<h3>How to determine the equation?</h3>
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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