a) Sketch a possible graph of a polynomial function that meets all of the following criteria: [4C]i. x → ∞o, y → - 00ii. Only has zeros at x =- 4(order 1),iii. Has y-intercept at y = 41(order 3), 3(order 2)b) Determine the equation of this polynomial function.-5-5-O-55

(a) The objective is to sketch a polynomial function which satisfies the given conditions. A…

Answered: a) Sketch a possible graph of a…

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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3. Sketch a rough graph of the following polynomial function, after describing the key characteristics of the function. f) = -2x(4 – 2x*)(x? - 1)? Degree Leading Coefficient (value) End Behaviour x -intercepts (including order) y-intercept What finite difference from the table of values of this function will be same and what will be its value?
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. f(x) = 8x³/2, a = 1; approximate 8(1.73/2) a. p₁(x) = b. p₂(x) = c. Using the linear approximating polynomial to estimate, 8 (1.73/2) is approximately (Simplify your answer.) Using the quadratic approximating polynomial to estimate, 8(1.73/2) is approximately. (Simplify your answer.)
C. Choose the letter of the correct answer. 1. Which of the following is an example of polynomial function? A. f(x) =+ 3x-1 B. ffx) = 2a2x 2. From the choices, which polynomial function in factored form represents the glven graph? A. f(x) = (x+2) px+1) (x-1) B. f(x) = (x-2) (x+1) (x-1) C. fx) = xpx+2) (x+1) (x-1) D. fx) = x(x-2) (x+1) (x-1) C. f6) = V7s-2x D. Fx) = x*+ V3-S 3. If you will draw the graph of y=x (x+2)a, how will you sketch it with respect to the x-ads A. Sketch it crossing both (-2, 0) and (0. 0). B. Sketch it crossing (-2, 0) and tangent at (0. 0). C. Sketch it tangent at (-2, 0) and crossing (0, 0). D. Sketch it tangent at both (-2, 0) and (0. 0). 4. Your classmate Linus encounters difficulties in showing a sketch of the graph of y = 2x + 3x2 -4x -6. You know that the quickest technique is the leading coefficient test. You want to help Linus In his problem. What hint/clue should you give A. The graph fols to the left and rises to the right. B. The graph rises to both…
12. For the polynomial p(x)=x²-2x²-x+2, determine the following then sketch the graph: a. Degree b. Roots including multiplicity End behavior C. d. y-intercept
For the following polynomial: f(x) = (x – 1)2 ( x2– x – 30) 3a) Describe the end behavior of the graph. (You 3b) Find the x and y-intercepts 3c) Is the graph of this function both smooth and continuous? Explain why or why not? 3d) Provide a sketch of the function. How did you use your answers to parts (a), (b), and (c) to sketch the graph.
7. Sketch a polynomial with the following properties. Degree: 6 Sign of leading coefficient: Positive Zeros: X = -3 order 1 x = -1 order x = 2 order 2 y intercept: 10
Pls help ASAP
4. a) Sketch a possible graph of a polynomial function that meets all of the following criteria: i. x→ ∞o, y →→ ∞ ii. Only has zeros at x = iii. Has y-intercept at y = 5 2(order 3), 1(order 1), 4(order 2) Determine the equation of this polynomial function. Show work. -5 5 0 -5 5
Show wheatear the statements are True or False (provide explanation/justification). a. sup A E A' b. If A is finite, then A C Ris closed. c. A CRis closed if and only if Ā = A.

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a) Sketch a possible graph of a polynomial function that meets all of the following criteria: [4C] i. x → ∞o, y →→ 00 ii. Only has zeros at x =- 4(order 1), 1(order 3), 3(order 2) iii. Has y-intercept at y = 4 b) Determine the equation of this polynomial function. -5 5 0 --5 10 5