# Math 3 - roberts(eer474 – HW 12 – windle –(56747 1...

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Unformatted text preview: roberts (eer474) – HW 12 – windle – (56747) 1 This print-out should have 14 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 6) 10.0 points If f is the polynomial function defined by f ( x ) = x 4- 2 x 2 + 5 x + 1 , (i) find the maximum number of turning points of the graph of f ; 1. max number = 1 2. max number = 5 3. max number = 3 correct 4. max number = 6 5. max number = 4 Explanation: The graph of a polynomial function of de- gree 4 can have at most 3 turning points. 002 (part 2 of 6) 10.0 points (ii) find the maximum number of x- intercepts of the graph of f ; 1. max number = 0 2. max number = 3 3. max number = 1 4. max number = 5 5. max number = 4 correct Explanation: A polynomial equation of degree 4 can have at most 4 real roots, so the number of x- intercepts the graph of a polynomial function of degree 4 can have is at most 4. 003 (part 3 of 6) 10.0 points (iii) find the minimum number of x- intercepts of the graph of f ; 1. min number = 6 2. min number = 5 3. min number = 0 correct 4. min number = 4 5. min number = 2 Explanation: If a polynomial function f has even degree, then lim x →∞ f ( x ) = lim x →-∞ f ( x ) , so its graph need not cross the x-axis. When the degree is even , therefore, the minimum number of x-intercepts is 0. On the other hand, when the degree is odd, lim x →∞ f ( x ) =- lim x →-∞ f ( x ) , so its graph must cross the x-axis. When the degree is odd, therefore, the minimum...
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Math 3 - roberts(eer474 – HW 12 – windle –(56747 1...

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