By William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Drawing on their many years of training adventure, William Briggs and Lyle Cochran have created a calculus textual content that includes the teacher’s voice past the school room. That voice—evident within the narrative, the figures, and the questions interspersed within the narrative—is a grasp instructor prime readers to deeper degrees of knowing. The authors entice readers’ geometric instinct to introduce primary strategies and lay the basis for the extra rigorous improvement that follows. finished workout units have acquired compliment for his or her creativity, caliber, and scope. This ebook is an increased model of Calculus: Early Transcendentals via an identical authors, with a complete bankruptcy dedicated to differential equations, extra sections on different issues, and extra workouts in such a lot sections.
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Additional resources for Calculus for Scientists and Engineers: Early Transcendentals
X - 2 x - 2 1 x 1 Therefore, the graph of f is identical to the graph of the line y = x - 3 when x ϶ 2. 22). b. 23 y ϭ x6 y x if x Ú 0 -x if x 6 0. 23. 24 ➤ 40 y ϭ x2 1 2 3 4 x 1. Power functions are a special case of polynomials; they have the form f 1x2 = x n, where n is a positive integer. 24). 25). Chapter 1 y • Functions y ϭ x7 QUICK CHECK 2 y ϭ x5 y ϭ x3 40 2. Root functions are a special case of algebraic functions; they have the form f 1x2 = x 1>n, where n 7 1 is a positive integer. Notice that when n is even (square roots, fourth roots, and so forth), the domain and range consist of nonnegative numbers.
2 Representing Functions 40. f 1t2 = t 2 23 y = ͉x͉. Find formulas for f and g. Verify your answers with a graphing utility. y y ϭ f (x) y 4 3 y ϭ ͉x͉ 2 1 1 0 1 2 3 4 5 6 7 8 t 1 x y ϭ g(x) 41. f 1t2 = e -2t + 8 if t … 3 2 if t 7 3 44. Transformations Use the graph of f in the figure to plot the following functions. a. y = -f 1x2 c. y = f 1x - 22 e. y = f 1x - 12 + 2 y 8 7 b. y = f 1x + 22 d. y = f 12x2 f. y = 2f 1x2 y 6 5 4 3 y ϭ f (x) 2 1 0 1 1 2 3 4 5 6 7 8 t 1 x 42. f 1t2 = ͉t - 2͉ + 1 45. Transformations of f 1x2 ؍x 2 Use shifts and scalings to transform the graph of f 1x2 = x 2 into the graph of g.
Therefore, the graph represents corresponds to a horizontal scaling and a vertical shift. It has the equation y = f 1ax2 - 1, where a = 12 . y = 1 1 f 1x2 - 1 = x 2 - 1. 42 How do you modify the graph of f 1x2 = 1>x to produce the graph of g1x2 = 1>1x + 42? QUICK CHECK 4 ➤ g1x2 = 2 Ηx + 12Η , which means the graph of g may also be obtained by a vertical scaling and a horizontal shift. EXAMPLE 9 Scaling and shifting Graph g1x2 = ͉2x + 1͉. SOLUTION We write the function as g1x2 = Η2 1 x + 2 Η . Letting f 1x2 = ͉x͉, we have g1x2 = f 1 2 1 x + 22 .