Analyze and graph a cubic function (Question 3, Hard)

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Q. The function f(x) is a cubic function given by:

f(x)=−x^3+3x+2 (Difficulty: Hard)

a) Factor f(x)
b) Find all zeros of f(x) and their multiplicity.
c) Find the domain and range of f(x)
d) Use the y intercept, x intercepts and other properties of the graph of to sketch the graph of f(x)

Recall: The rational zero theorem tells us that if r⁆ is a rational zero of f(x)⁆, then r⁆ is of the form ±p/q⁆, where p⁆ is a factor of the constant term, and q⁆ is a factor of the leading coefficient.

Remainder theorem: If the polynomial f(x)⁆ is divided by x−c⁆ (where c⁆ is a constant), then the remainder is f(c)⁆.

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