If any of the factors of a polynomial function are linear, then which of the followingis NOT true?A. The graph has a linear shape near this x-intercept.B. The x-intercept is a point where the curve passes through the x-axis.C. The x-axis is tangent to the curve at these points.D. The zeros of the function are locations on the graph where y = 0.

It is provided that the polynomial function has linear factors. We need to determine the statement…

Answered: If any of the factors of a polynomial…

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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Determine the lease possible degree of the polynomial function shown.
1. If any of the linear factors of a polynomial function are squared, then which of the following is not true o corresponding x-intercepts? The x-intercepts are turning points of the curve. b. a. The x-axis is tangent to the curve at these points. The graph passes through the x-axis at these points. d. с. The graph has a parabolic shape near these x-intercepts. 2. Which graph is a possible sketch of the function g(x) = (x+ 1) (x- 2)? 30+ 30 + 24 + 24 + 18+ 18- 12+ 12- 6+ 6+ +%> 3 4 5 -54 -3 -2 -6+ 2 -5 -4 -3 3 4. -6+ -12- -12 + -18+ -18 + -24 + --24 + -30- -30+ a. с. 个) 30+ 30 24+ 24 - 18+ 18+ 12+ 12+ 6+ 6- ++ -5 -4 -3 -2 /-1 -6 I 2 3 4 5 x -5 4 -3 -2 -1 -6+ 2 3 4 5 x -12+ -12+ -18 + -18+ -24 - -24 + -30+ b. -30 + d. 3. Which equation is a quartic function with zeros at-4,-1, 2, 3? a. y = (x-4)(x – 1)(x+2)(x +3) b. y = (x-2)(x- 3)(x+4)(x+1) c. y = (x+4) (x + 1)(x – 2)°(x – 3) d. y= (x+4) (x + 1)°(x – 2)°(x – 3)²
1. Which statement BEST describes the attributes of the graph of the function y = x- &r 20? A. The function has zeros at (10, 0), and (-2, 0), and has a vertex at (4, –36). B. The function has zeros at (-10, 0), and (-2, 0), and has a vertex at (-4,-36). C. The function has zeros at (10, 0), and (-2, 0), and has a vertex at (-4, -36). D. The function has zeros at (-10, 0), and (2, 0), and has a vertex at (4, -36). 2. Sy =x²-6x+8 ? x-y=-2 What are the solutions of the system of equations A. (5, 3) and (2,0) B. (6, 8) and (1, 3) C. (-6, -4) and (-1, 1) D. (-5, -7) and (-2, -4)
7. The function shown is a second-order piecewise polynomial, plot the function yourself: 22 y 20 18 16 14 12 10 8 6 0 1 2 3 4 X 10 5 6 7 8
4. For each graph below, answer the following. a. Is the polynomial an even or odd degree polynomial? b. Is the leading coefficient positive or negative. c. State the end behavior of the function, ie as zoo, y → ? and as z →-∞, y → ? d. State each zero (z-intercept) in point form with its multiplicity. Note the overall degree of the polynomial listed with the graph. e. State the y-intercept in point form. f. Find a possible formula for the graph using your answers above. Remember to find the leading coefficient, using either the y-intercept or another point on the graph. g. As always, please discuss each with your group, and make sure you agree on your answers. Share your work. H (050) Sixth Degree Polynomial Seventh Degree Polynomial
The table below shows data on the number of employees that a small company had from 1975 to 2000. Year 1975 1980 1985 1990 1995 2000 # of 50 65 70 60 55 44 Employees Let 0 represent the year 1975. Find a quadratic model for this function. .2 y = ax + bx + c Using the above equation, fill in the coefficients for a, b, and c rounding all decimals to the hundredths place.
Below is a polynomial function. You can assume that you see all x-intercepts. 100 50 A 2 --50 True or False: the degree of this polynomial is even b. Give all points which are relative extrema. а. C. Give all inflection points d. Give all x-intercepts е. Give all y-intercepts f. Between which points is the function increasing? Between which points is the function decreasing? h. Explain why this could not be a 3rd degree polynomial g.
Use the given information about the polynomial graph to write the equation. Degree 3. Zeros at z = - 3, x = - 1, and æ = 1. y-intercept at (0, 9). f(x) = Preview

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