In Problems 11–26, graph each of the functions using the graphs of functions f and g below. f(x) g(x) -5 11. y = f(x) + 2 12. y = g(x) – 1 13. y = f(x + 2) 14. y = g(x – 1) 15. у %3D 8 (х — 3) 16. y = f(x + 3) 17. y = g(x) – 3 18. y = f(x) + 3 19. у 3D -(х) 20. y = -g(x) 21. y = 0.5g(x) 22. у %3D 2/(х) %3D
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I need help with question #21 and #22, I don't know how to graph those and I don't understand it. Can please explain step by step.
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- 2. Let P(t) represent the population of Los Angeles t years after 1900. (a) Interpret P(10) = 319, 198 in words. P(10) - Р(0) (b) Given that P(0) = 102, 479 and P(10) = 319, 198, calculate and interpret 10 – 0 in words. (c) of Los Angeles reached 200,000. Set up an equation that could be used to find how many years after 1900 the populationIn Problems 23–28, answer the questions about the given function. x² + 2 26. f(x) = x + 4 23. f(x) = 2x? - x - 1 (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -1, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. 24. f(x) = -3x² + 5x (a) Is the point (-1, 2) on the graph of f? (b) If x = -2, what is f(x)? What point is on the graph of f? (c) If f(x) = -2, what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if any, of the graph of f. (f) List the y-intercept, if there is one, of the graph of f. x + 2 (a) Is the point ( 1,) on the graph of f? (b) If x = 0, what is f(x)? What point is on the graph of f? (c) If f(x) =5. what is x? What point(s) are on the graph of f? (d) What is the domain of f? (e) List the x-intercepts, if…In Problems 93–104, graph each polynomial function. 93. f(x) = x + 2r? - 5x - 6 94. f(x) = x' + &r? + 11x – 20 95. f(x) = 2x –x² + 2r – 1 96. f(x) = 2r + x² + 2x + 1 97. f(x) = x* + x² - 2 98. f(x) = x - 3x² – 4 %3D %3D 99. f(x) = 4x* + 7x? – 2 100. f(x) = 4xr + 15x? - 4 101. f(x) = x* + x³ - 3x² - x + 2 %3D %3D %3D 102. f(x) = x* - x - 6r? + 4x + 8 103. f(x) 4x5 - 8x - x + 2 104. f(x) = 4xs + 12x - x - 3
- In Problems 23–30, use the given zero to find the remaining zeros of each function. 23. f(x) = x - 4x² + 4x – 16; zero: 2i 24. g(x) = x + 3x? + 25x + 75; zero: -5i 25. f(x) = 2x* + 5x + 5x? + 20x – 12; zero: -2i 26. h(x) = 3x4 + 5x + 25x? + 45x – 18; zero: 3i %3D 27. h(x) = x* – 9x + 21x? + 21x – 130; zero: 3 - 2i 29. h(x) = 3x³ + 2x* + 15x³ + 10x2 – 528x – 352; zero: -4i 28. f(x) = x* – 7x + 14x2 – 38x – 60; zero:1 + 3i 30. g(x) = 2x – 3x* – 5x – 15x² – 207x + 108; zero: 3i3. Three functions are shown: f(x) = (x + 2)² – 2, g(x), and h(x). Determine an equation for g(x) and h(x) in the same form as f(x). f(x) = (x + 2)²2 XXX 2 Answer: (4) h(x) g(x)/what is the equation f(x)= a (x-h) + k with the appropriate shifts entered
- In Problems 27–36, verify that the functions f and g are inverses of each other by showing that f(g(x)) = x and g(f(x)) any values of x that need to be excluded. = x. Give 27. f(x) = 3x + 4; g(x) = (x- 4) 28. f(x) = 3 – 2x; g(x) = -(x – 3) 29. f(x) = 4x – 8; 8(x) = + 2 30. f(x) = 2x + 6; 8(x) = ;x - 3 31. f(x) = x' - 8; g(x)· Vx + 8 32. f(x) = (x – 2)², 2; g(x) = Vĩ + 2 33. f(x) = ; 8(x) = 34. f(x) = x; g(x) x - 5 2x + 3' 2x + 3 4x - 3 3x + 5 35. f(x) *: 8(x) = 8(x) 36. f(x) = 1- 2x x + 4 2 - x 1.7 82 CHAPTER 1 Graphs and Functions In Problems 37-42, the graph of a one-to-one function f is given. Draw the graph of the inverse function f"1. For convenience (and as a hint), the graph of y = x is also given. 37. y= X 38. 39. y =X 3 (1, 2), (0, 1) (-1,0) (2. ) (2, 1) (1, 0) 3 X (0, -1) -3 (-1, -1) 3 X -3 (-2, -2) (-2, -2) -하 -하 -하 40. 41. y = x 42. y = X (-2, 1). -3 3 X (1, -1)In Problems 13–24, use the graph of the function f given.In Problems 33–44, determine algebraically whether each function is even, odd, or neither. 34. f(x) = 2x* –x? 38. G(x) = Vĩ 33. f(x) = 4x 37. F(x) = V 35. g(x) = -3x² – 5 39. f(x) = x + |x| 36. h (х) — Зx3 + 5 40. f(x) = V2r²+ 1 x² + 3 -x 42. h(x) =- 1 2x 44. F(x) 41. g(x) 43. h(x) x2 - 1 3x2 - 9
- If the point (1,4) lies on the graph of y = f(x), then the y-coordinate of the corresponding point on the graph of the transformed function y = 2f(4x) is Answer:4) The number of snakes on Snake Island in Georgian Bay any year is dependent on two sources. Every year, through reproduction, the number of snakes on the island increase by 40 individuals. Snakes caught on other islands are also transplanted to Snake Island. The frequency of transplantation depends on the year and can be modelled by the function g(x)=10sin x+30, where g(x) represents the number of individuals transplanted in year x. Determine a function that will model the population of snakes on the island and takes into account both reproduction and transplantation. π 63. Find f(g(z)) and g(f(x)) for the pair of functions. f(x) =# +1 g(z) =4x-17 (a)6) f(g(z)) = .4. g(f(x)) =