3. Draw the graph of a polynomial function that satisfies the following conditions.
f(-1) = -3 and f(0) = 0.
f(x) is increasing on (-∞, -2), (-1,1) and (2, ∞o).
f(x) is decreasing on (-2,-1) and (1,2).
• f(x) is concave up on (-1.5,0) and (1.5, ∞).
f(x) is concave down on (-∞, -1.5) and (0,1.5).
• As x→∞ f (x) → ∞.
• As x→∞ f (x) → -∞.
(a) Explain how your graph satisfies each condition.
(b) Explain what is the smallest degree possible for the polynomial function f(x).
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