In Exercises 15–18, use the Leading Coefficient Test to determinethe end behavior of the graph of the given polynomial function.Then use this end behavior to match the polynomial function withits graph. [The graphs are labeled (a) through (d).]16. f(x) = x³ – 4x²18. f(x) = -x - x² + 5x – 315. f(x) = -x* + x?%3D17. f(x) = (x – 3a.b.101-8-264-2-4+2-2 4 6C.yd.-4 2

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Answered: In Exercises 15–18, use the Leading…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Complex Numbers

Section4.2: Complex Solutions Of Equations

Problem 6ECP: Find a fourth-degree polynomial function f with real coefficients that has 2, 2, and 7i as zeros.

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In Exercises 12–20, find all zeros of each polynomial function. Then graph the function. 12. f(x) = (x – 2)°(x + 1)³ 13. f(x) = -(x – 2)(x + 1)? 14. f(x) = x - xr? – 4x + 4 15. f(x) = x* - 5x² + 4 16. f(x) = -(x + 1)° 17. f(x) = -6x³ + 7x? - 1 18. f(x) = 2r³ – 2x 19. f(x) = x - 2x² + 26x 20. f(x) = -x + 5x² – 5x – 3 %3D %3D %3! %3D %3!
In Exercises 16–17, find the zeros for each polynomial function and give the multiplicity of each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. 1)(x + 2)²(x + 5)³ 25x+125 16. f(x) = -2(x 17. f(x) = x³ - 5x²
In Exercises 1–10, determine which functions are polynomial functions. For those that are, identify the degree. 2. f(x)=7x2 +9x4 3. g(x) = 7x5 - px3 + 1/5x 5. h(x) = 7x3 +2x2 + 1/x 7. f(x)=x1/2 -3x2 +5
In Exercises 130–133, use a graphing utility to graph the functions y, and y2. Select a viewing rectangle that is large enough to show the end behavior of y2. What can you conclude? Verify your conclusions using polynomial multiplication. 130. yı = (x - 2)² y2 = x2 – 4x + 4 131. yı = (x – 4)(x² y2 = x - 7x2 + 14x – 8 132. yı = (x – 1)(x + x + 1) y2 = x – 1 133. yı = (x + 1.5)(x – 1.5) y2 = x? – 2.25 3x + 2)
In Exercises 26–31, find an nth-degree polynomial function with real coefficients satisfying the given conditions. If you are using a graphing utility, use it to graph the function and verify the real zeros and the given function value. 26. n= 3; 4 and 2i are zeros; f(-1) = -50 31. n= 4; -2, 5, and 3 + 2i are zeros; f(1) = -96
In Exercises 25–32, find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the xaxis, or touches the xaxis and turns around, at each zero. 28. f(x) = -31x + 1/2(x - 4)3 29. f(x)=x3 -2x2 +x30. f(x)=x3 +4x2 +4x31. f(x)=x3 +7x2 -4x-28 32. f(x)=x3 +5x2 -9x-45
In Exercises 35–42, find all real values of x for which fx0. f(x)=4x+6
For Exercises 69–84, find the zeros and their multiplicities. Consider using Descartes' rule of signs and the upper and lower bound theorem to limit your search for rational zeros. (See Example 10) 69. f(x) = 8x – 42x + 33x + 28 (Hint: See Exercise 61.) 6x – x? (Hint: See Exercise 62.) 70. f(x) - 57x + 70 72. f(x) = 3x – 16x + 5x + 90x (Hint: See Exercise 64.) 2x + 11x - 63x? - 50x + 40 71. f(x) = (Hint: See Exercise 63.) - 138x + 36
For Exercises 23–24, use the remainder theorem to determine if the given number c is a zero of the polynomial. 23. f(x) = 3x + 13x + 2x + 52x – 40 a. c = 2 b. c = 24. f(x) = x* + 6x + 9x? + 24x + 20 а. с 3D —5 b. c = 2i
In Exercises 1–16, divide using long division. State the quotient, q(x), and the remainder, r(x). 18x4 + 9x3 + 3x2 /3x2+1 In Exercises 17–25, divide using synthetic division. 17. (2x2 +x-10)/(x-2) 25. (x2 -5x-5x3 +x4)/(5+x)
Exercises 103–110: Let the domain of f(x) be [-1,2] and the range be [0, 3 ]. Find the domain and range of the following. 103. f(x – 2) 104. 5/(x + 1) 105. -/(x) 106. f(x – 3) + 1 107. f(2x) 108. 2f(x – 1) 109. f(-x) 110. -2/(-x)
What is the formula for w(x), the node polynomial?

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