By Ron Larson, Bruce H. Edwards
The one Variable component to Calculus: Early Transcendental capabilities, 5/e, deals scholars cutting edge studying assets. each variation from the 1st to the 5th of Calculus: Early Transcendental services, 5/e has made the mastery of conventional calculus abilities a concern, whereas embracing the easiest good points of recent know-how and, while applicable, calculus reform rules.
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Additional resources for Calculus of a Single Variable: Early Transcendental Functions
F ͑x͒ ϭ 29. f ͑x͒ ϭ (a) g͑0͒ 11. f ͑x͒ ϭ 27. f ͑x͒ ϭ (a) f ͑Ϫ1͒ 3. f ͑x͒ ϭ 7x Ϫ 4 1 In Exercises 27– 30, evaluate the function as indicated. Determine its domain and range. (b) f ͑0͒ In Exercises 31–38, sketch a graph of the function and find its domain and range. Use a graphing utility to verify your graph. 31. f ͑x͒ ϭ 4 Ϫ x 32. g͑x͒ ϭ 4 x 33. h͑x͒ ϭ Ίx Ϫ 6 1 34. f ͑x͒ ϭ 4 x3 ϩ 3 35. f ͑x͒ ϭ Ί9 Ϫ 36. f ͑x͒ ϭ x ϩ Ί4 Ϫ x 2 x2 37. g͑t͒ ϭ 3 sin t 38. h͑͒ ϭ Ϫ5 cos 2 WRITING ABOUT CONCEPTS 39. The graph of the distance that a student drives in a 10-minute trip to school is shown in the figure.
SLOPE-INTERCEPT FORM OF THE EQUATION OF A LINE The graph of the linear equation y ϭ mx ϩ b is a line having a slope of m and a y-intercept at ͑0, b͒. EXAMPLE 3 Sketching Lines in the Plane Sketch the graph of each equation. a. y ϭ 2x ϩ 1 b. y ϭ 2 c. 3y ϩ x Ϫ 6 ϭ 0 Solution a. Because b ϭ 1, the y-intercept is ͑0, 1͒. 18(a). b. Because b ϭ 2, the y-intercept is ͑0, 2͒. 18(b). c. Begin by writing the equation in slope-intercept form. 3y ϩ x Ϫ 6 ϭ 0 3y ϭ Ϫx ϩ 6 1 yϭϪ xϩ2 3 Write original equation.
4, 9͒ 75. The graphs of f, g, and h are shown in the figure. Decide whether each function is even, odd, or neither. f Functions and Their Graphs 2 x 4 −6 −4 −2 x 2 4 6 −4 g −6 Figure for 76 76. The domain of the function f shown in the figure is Ϫ6 Յ x Յ 6. (a) Complete the graph of f given that f is even. (b) Complete the graph of f given that f is odd. (b) The thermostat is reprogrammed to produce a temperature H͑t͒ ϭ T͑t Ϫ 1͒. How does this change the temperature? Explain. (c) The thermostat is reprogrammed to produce a temperature H͑t͒ ϭ T͑t͒ Ϫ 1.
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