Homework 1. 3x 12, 61.P (x) = 3t 21 Section 1.2
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1 Section 1.1 Homework 1 (34, 36) Determine whether the equation defines y as a function of x. 34. x + h 2 = 1, 36. y = 3x 1 x + 2. (40, 44) Find the following for each function: (a) f(0) (b) f(1) (c) f( 1) (d) f( x) (e) f(x) (f) f(x + 1) (g) f(2x) (h) f(x + h) 40. f(x) = 2x 2 + x 1, 44. f(x) = x 2 + x (54, 55, 61) Find the domain of each function. 54. G(x) = x + 4 x 3 4x, 55. h(x) = t 4 3x 12, 61.P (x) = 3t 21 Section f(x) = x2 + 2 x + ( 4 (a) Is the point 1, 3 ) on the graph of f? 5 (b) If x = 0, what is f(x)? What point is on the graph of f? (c) If f(x) = 1, what is x? What point(s) is (are) on the graph of f? 2 (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. (g) What are the zeros of f? Section 1.3 (25, 26, 27)The graph of a function is given. Use the graph to find: (a) The intercepts, if any (b) The domain and range (c) The intervals on which the function is increasing, decreasing, or constant (d) Whether the function is even, odd, or neither (36, 39, 42) Determine algebraically whether each function is even, odd, or neither. 36. h(x) = 3x 2 + 5, 39. f(x) = x + x, 42. h(x) = x x 2 1 1
2 2 Section (a) Find the domain of each function. (b) Locate any intercepts. (c) Graph each function. (d) Based on the graph, find the range. (e) Is f continuous on its domain? f(x) = f(x) = { x if 2 x < 0 x 3 if x 0 { 2 x if 3 x < 1 x if x 1 Section Find the function that is finally graphed after each of the following transformations is applied to the graph of y = x in the order stated. (1) Reflect about the x axis (2) Shift right 3 units (3) Shift down 2 units 32. If (3, 6) is a point on the graph of y = f(x), which of the following points must be on the graph of y = f( x)? (a) (6, 3) (b) (6, 3) (c) (3, 6) (d) ( 3, 6) The graph of a function f is illustrated. Use the graph of f as the first step toward graphing each of the following functions : (a) F (x) = f(x) + 3 (b) G(x) = f(x + 2) (c) P (x) = f(x) (d) H(x) = f(x + 1) 2 (e) Q(x) = 1 f(x) (f) g(x) = f( x) (g) h(x) = f(2x) 2 Section 2.1 (18, 20) A linear function is given. (a) Determine the slope and y intercept of each function.
3 3 (b) Use the slope and y intercept to graph the linear function. (d) Determine whether the linear function is increasing, decreasing, or constant. 18. h(x) = 2 x + 4, 20. G(x) = (Cost Function) The simplest cost function is the linear cost function, C(x) = mx + b, where the y intercept b represents the fixed costs of operating a business and the slope m represents the cost of each item produced. Suppose that a small bicycle manufacturer has daily fixed costs of $1800, and each bicycle costs $90 to manufacture. (a) Write a linear model that expresses the cost C of manufacturing x bicycles in a day. (b) Graph the model. (c) What is the cost of manufacturing 14 bicycles in a day? (d) How many bicycles could be manufactured for $3780? Section 2.3 (80, 85) Find the real zeros of each quadratic function using any method you wish. What are the x intercepts, if any, of the graph of the function? 80. f(x) = 6x 2 + 7x 20, 85. f(x) = x 2 + x Solve f(x) = g(x). What are the points of intersection of the graphs of the two functions? f(x) = 10x(x + 2) g(x) = 3x Suppose that f(x) = x 2 3x 18 and g(x) = x 2 + 2x 3. (a) Find the zeros of (f + g)(x). (b) Find the zeros of (f g)(x). (c) Find the zeros of f g(x) A ball is thrown vertically upward from the top of a building 96 feet tall with an initial velocity of 80 feet per second. The distance s (in feet) of the ball from the ground after t seconds is s(t) = t 16t 2. (a) After how many seconds does the ball strike the ground? (b) After how many seconds will the ball pass the top of the building on its way down? Section 2.4 (27, 30) Graph the function f by starting with the graph of y = x 2 and using transformations. Hint : If necessary, write f in the form f(x) = a(x h) 2 + k. 27. f(x) = x 2 2x, 30. f(x) = 3x x (a) Graph the function by determining whether its graph opens up or down and by finding its vertex, axis of symmetry, y intercept, and x intercepts, if any.
4 4 (b) Determine the domain and the range of the function. (c) Determine where the function if increasing and where it is decreasing. f(x) = 4x 2 2x Determine the quadratic function whose graph is given. (56, 58) Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value, and then find the value. 56. f(x) = 2x 2 + 8x + 3, 58. f(x) = 4x 2 4x 84. The John Deere company has found that the revenue, in dollars, from sales of heavy-duty tractors is a function of the unit price p, in dollars, that it charges. If the revenue R is R(p) = 1 2 p p what unit price p should be charged to maximize revenue? What is the maximum revenue? Section Use the graph of the function given to solve each problem. f(x) = x 2 ; g(x) = 2 (a) f(x) = g(x) (b) f(x) g(x) (c) f(x) > g(x) (28, 30, 32) Solve each equation x = 9, 30. x = 1, ν = 1
5 5 48. Solve each absolute value inequality. Expres syour answer using set-builder or interval notation. Graph the solution set. x < 5 Section Determine which functions are polynomial functions. For those that are, state the degree. For those that are not, tell why not. Write each polynomial in standard form. Then identify the leading term and the constant term. 19. f(x) = 1 1 x, 20. f(x) = x(x 1), 21. g(x) = x3/2 x 2 + 2, 22. h(x) = x( x 1), 23. f(x) = 5x 4 πx (37, 40) Use transformations of the graph of y = x 4 or y = x 5 to graph each function. 37. f(x) = 2(x + 1) 4 + 1, 40. f(x) = 3 (x + 2) 4 (56, 57, 59) For each polynomial function: (a) List each real zero and its mulitplicity. (b) Determine whether the graph crosses or touches the x axis at each x intercept. (c) Determine maximum number of turning points on the graph. (d) Determine the end behavior. 56. f(x) = (x + 3) 2 (x 2) 4, 57. f(x) = 3(x 2 + 8)(x 2 + 9) 2, 59. f(x) = 2x 2 (x 2 2) (66, 68) Construct a polynomial function that might have the given graph. (80, 110) Analyze each polynomial function by following Steps 1 through 5 on page f(x) = (3 x)(2 + x)(x + 1), 110. f(x) = 4x x 2 4x 10
6 Construct a polynomial function f with the given characteristics. Zeroes: -4, -1, 2; degree: 3; y intercept: 16
7 7 References [1] Precalculus, 3rd Edition, Michael Sullivan and Michael Sullivan, III.
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