Answer:
none of the above
best choice: D
Explanation:
You want a possible function for the given graph.
Zeros
The graph shows a function with zeros at -2, +2, and +5. The multiplicity of the zero at -2 is even, which is why the x-axis is not crossed there.
The graph shows a function with odd multiplicity of the zeros at +2 and +5. However, an odd exponent greater than 1 will produce a "flat spot" at the zero crossing. There isn't one at either place, so we must conclude ...
sadly, None of the Above
Best choice
The only function choice with a factor of (x+2) having even multiplicity is ...
D. f(x) = (x + 2)²(x-2)(x - 5)³
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Additional comment
The attached graph shows an approximation of the given graph by ...
f(x) = (x +2)²(x -2)(x -5)/10.5
The vertical scaling is necessary to get the peaks near where they are shown.
The second attachment shows a scaled version of function D. Its relative peak values are all wrong, along with the zero crossing at x=5 and the vertical scaling.