In Exercises 73–74, use the graph of the rational function to solve each inequality. flx) = + 1 [-4, 4, 1] by [-4, 4, 1] 1 1 73. 4(x + 2) 4(x – 2) 74. 4(x + 2) 4(x - 2)
Q: In Exercises 70-74, use the graph of y = f(x) to graph each function g. y 4 3 2- -4-2 23 4 3+ y =…
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Q: A and Bare open and bounded.
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A: Given g(x) = -2x2 +x -1 [-3, 5] Absolute maximum occur where g'(x) = 0 or at the end…
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A: Topic = Application of derivative Absolute maximum value is 15.
Q: Identify the vertex of: f (x) - 4 = (x + 1)² || | O (-4, 1) O (1, –4) O (-1, -4) O (-1, 4)
A: To find the vertex of function
Q: (b) Express in rational form the generating function of 2, -2/5, 2/25, -2/125, 2/625,..
A: The given problem is to find the generating function for the given sequence, we can observe same…
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A: Givenx+1x+3<0solve the following rational inequality for x
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Q: Example 2: Determine the vertex of f(x) = x² -5x +6 %3D
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Q: g'(x) = g(x)=√x - Be*
A: Differenciate wrt x
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Q: Exercises 1–10: Express the following in interval notation. 1. x < 2 3. x 2 - 1 5. {x | 1 s x < 8}
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A: To Sketch the graph of function f(x)=16x3-32x2+5x+1
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Q: EXERCISE 6 (PSAT – 20151028 Section 4, Q9) (Calculator permitted) f (x) = x2 + 4(x – 3) Which of the…
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Q: Summarize the pertinent information obtained by applying the graphing strategy and sketch the graph…
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Q: In Exercises 5–8, determine whether the graph of the function is symmetricabout the y-axis, the…
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Q: Let ƒ( θ) = θ3 - 2 θ + 2.Use the Intermediate Value Theorem to show that ƒ has a zero between -2 and…
A: Intermediate Value Theorem: Let f(x) be a polynomial function then intermediate value theorem states…
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Q: 2 is the graph of f(x) = -2/3 x – 3. -6 -5 -4 -3 -2 -10 1 2 3456 -2 -3 -4 -5 O False True
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A: Solution :-
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A: First list some coordinates for the given relation as shown in below table.
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Q: Sketch the graph of the function f(x) = x³ – 2x² – 5x + 6 using calculus – based analysis. -
A: Given problem:- Sketch the graph of the function f(x) = x3 – 2x2 − 5x + - 6 using calculus - based…
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A: 13. f(x)=(x+2)(x-2) 14. g(x)=1(x+2)(x-2)
Q: V21. Show that there exist constants M and N such that M||x||| < ||||2< N ||x|| -
A: Given ||x||1=∑i=1n|xi|=|x1|+|x2|+...+|xn| ||x||2=∑i=1n|xi|2=|x1|2+|x2|2+...+|xn|2 Now we have…
Q: In Exercises 41 and 42, (a) write formulas for ƒ ∘ g and g ∘ ƒ and find the (b) domain and (c) range…
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Q: In Exercises 7–10, write a formula for ƒ ∘ g ∘ h. 7. ƒ(x) = x + 1, g(x) = 3x, h(x) = 4 - x 8. ƒ(x)…
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- In Exercises 139–142, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. x2 – 25 = x - 5 5 139. X - x? + 7 140. = x? + 1 7 7 domain of f(x) = is x(x – 3) + 5(x - 3) 141. The (-0, 3) U (3, 0). 142. The restrictions on the values of x when performing the division f(x) h(x) g(x) k (x) are g(x) + 0, k(x) # 0, and h(x) + 0.In Exercises 15 – 28, a function f(x) is given.(a) Find the possible points of inflection of f.(b) Create a number line to determine the intervals onwhich f is concave up or concave down.16. f(x) = −x^2 − 5x + 7Exercises 35–42: Write the given expression in the form f(x) = a(x – h)² + k. Identify the vertex. 35. f(x) = x² - 3x 36. f(x) = x² – 7x + 5 37. f(x) = 2x² – 5x + 3 38. flx) = 3x² + 6x + 2 39. f(x) = 2x² – &x – 1 40. f(x) = --² - x 41. f(x) = 2 – 6x – 3x 42. f(x) = 6 + 5x – 10x?
- In Exercises 126–131, use a graphing utility to graph each function. Use a [-5, 5, 1] by [-5, 5, 1] viewing rectangle. Then find the intervals on which the function is increasing, decreasing,. or constant. 126. f(x) = x' – 6x² + 9x + 1 127. g(x) = |4 – x²| 128. h(x) = |x – 2| + |x + 2| 129. f(x) = x*(x – 4) 130. g(x) = x 131. h(x) = 2 –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)In Exercises 31–32, each function is defined by two equations. The equation in the first row gives the output for negative numbers in the domain. The equation in the second row gives the output for nonnegative numbers in the domain. Find the indicated function values. S3x + 5 ifx 0 31. f(x) = а. f(-2) b. f(0) с. f(3) d. f(-100) + f(100)
- True or False The x-intercepts of the graph of a functiony = f1x2 are the real solutions of the equation f1x2 = 0.(pp. 73–75)Write an equation of the form f(x) = a* +b from the given graph. Then compute f(2). 8- 7- 6- f(x) |(1,6.3) 5- 4- 3- 10.2) X -4 -3 -2 -11- 3 4 f(x) = (Use integers or decimals for any numbers in the expression.)For Exercises 57–62, find and simplify f(x + h). (See Example 6) 59. f(x) = 7 – 3x 62. f(x) = x – 4x + 2 57. f(x) = -4x – 5x + 2 58. f(x) = -2x² + 6x – 3 60. f(x) = 11 – 5x² 61. f(x) = x' + 2x – 5
- a) Find the domain of f, g, f + g, f – & fg, ff, f/ g b) Find (f + g)(x), (f – g)(x), (fg)(x), (ff)(x), For each pair of functions in Exercises 17–32: 15. (8 and g/f. Find f+ g)(x), (f – g)(x), (fg)(x), (ff)(x), (f/8)(x), and (g/f)(x). 17. f(x) = 2x + 3, g(x) = 3 – 5x %3D 18. f(x) = -x + 1, g(x) = 4x – 2 19. f(x) = x – 3, g(x) = Vx + 4 20. f(x) = x + 2, g(x) = Vx – 1 21. f(x) = 2x – 1, g(x) = – 2x² 22. f(x) = x² – 1, g(x) = 2x + 5 23. f(x) = Vx – 3, g(x) : = Vx + 3Each of Exercises 25–36 gives a formula for a function y = f(x). In each case, find f-x) and identify the domain and range of f-. As a check, show that f(fx)) = f-"f(x)) = x. 25. f(x) = x 26. f(x) = x, x20 %3D %3D 27. f(x) = x + 1 28. f(x) = (1/2)x – 7/2 30. f(x) = 1/r, x * 0 %3D 29. f(x) = 1/x, x>0 x + 3 31. f(x) 32. f(x) = VE - 3 34. f(x) = (2x + 1)/5 2 33. f(x) = x - 2r, xs1 (Hint: Complete the square.) * + b x - 2' 35. f(x) = b>-2 and constant 36. f(x) = x? 2bx, b> 0 and constant, xsbExercises 1-6: Identify f as being linear, quadratic, or neither. If f is quadratic, identify the leading coefficient a and evaluate f(-2). 1. f(x) = 1 – 2x + 3x? 2. f(x) = -5x + 11 3. f(x) = - x 4. f(x) = (x² + 1)² 5. f(x) = } - * 6. f(x) = }r?