[F-ItemA] Direction: Kindly answer the given questions completely and correctly. Any missing answer will result to DISLIKING your solutions. Note: Please answer all questions. Graphing a Polynomial FunctionTo sketch the graph of a polynomial function we need to consider the following:A. leading termB. behavior of the graphThe graph of a polynomial function:1. comes down from the extreme left and goes up to the extreme right if n is even and an>0.2. comes up from the extreme left and goes up to the extreme right if n is odd and an>0.3. comes up from the extreme left and goes down to the extreme right if n is even and an<0.4. comes down from the extreme left and goes down to the extreme right if n is odd and an<0.a>0an <0n is evenn is odd~ ~C. x-interceptsD. multiplicity of rootsIf r is a zero of odd multiplicity, the graph of P(x) crosses the x-axis at r.if r is a zero of even multiplicity, the graph of P(x) is tangent to the x-axis at r.E.y-interceptF. number of turning pointsTurning points are points where the graph from increasing to decreasing function value, or vice versa. The number of turning pointsin the graph of a polynomial is strictly less than the degree of the polynomial. Also, we must note that;1. Quartic Functions: have an odd number of turning points; at most 3 turning points2. Quintic functions: have an even number of turning points, at most 4 turning points3. The number of turning points is at most (n-1). 4. y=-(x+2)(x+1)²(x−3)A. leading term:B. behavior of the graph:(nisand an_0)C. x-intercepts:the polynomial in factored form isy=D. multiplicity of roots:_E. y-intercept:_F. number of turning points:G. sketch:

Given function y=-(x+2)(x+1)(x-3)

4. y=-(x+2)(x+1)²(x−3) A. leading term: B. behavior of the graph: (n is __________ and an_0) C. x-intercepts: the polynomial in factored form is y= D. multiplicity of roots:_ E. y-intercept:_ F. number of turning points: G. sketch:

4. y=-(x+2)(x+1)²(x−3) A. leading term: B. behavior of the graph: (n is __________ and an_0) C. x-intercepts: the polynomial in factored form is y= D. multiplicity of roots:_ E. y-intercept:_ F. number of turning points: G. sketch:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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