By Laura Taalman, Peter Kohn

Many calculus textbooks glance to interact scholars with margin notes, anecdotes, and different units. yet many teachers locate those distracting, who prefer to captivate their technology and engineering scholars with the wonderful thing about the calculus itself. Taalman and Kohn’s clean new textbook is designed to assist teachers do exactly that.

Taalman and Kohn’s Calculus bargains a streamlined, dependent exposition of calculus that mixes the readability of vintage textbooks with a contemporary standpoint on techniques, abilities, purposes, and conception. Its glossy, uncluttered layout removes sidebars, old biographies, and asides to maintain scholars all for what’s so much important—the foundational ideas of calculus which are so vital to their destiny educational careers.

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9. Consider the function f (x) = x 2 + 1. (a) Explain why y = 5 is in the range of f . (b) Explain why y = 0 is not in the range of f . (c) Argue that the range of f (x) = x 2 + 1 is [1, ∞). 10. Determine whether or not each diagram that follows represents a function. If it does, find its domain and range, and determine whether it is one-to-one. If it does not, explain what goes wrong. f g h 1 5 1 5 1 5 2 6 2 6 2 6 3 7 3 7 3 7 4 8 4 8 4 8 11. Construct a rule f : {2, 4, 6, 8, 10} → {1, 2, 3, 4} that is a function.

Complete the entries in the following table two ways: (a) to make an even function and (b) to make an odd function: 1 , what is f (x)? x2 + 1 1 (b) If h(x) = x 2 − 1 and h(l(x)) = 4 − 1, what is l(x)? x 1 1 (c) If u(x) = and y(u(x)) = , what is y(x)? 1−x 1−x (a) If g(x) = x 2 and f ( g(x)) = y = f (x) 11. If f (0) = 2, can f be an odd function? What if f (0) is undefined? Explain your answers. 12. Determine graphically whether each of the following four functions is even, odd, or neither. 1 f +g 7.

Write your answers in interval notation (or, if the solution is a discrete set of points, a list of those points). x =0 x−2 x 3 − 5x 2 + 6x < 0 x >0 x−2 x 3 − 5x 2 + 6x = 0 Concepts 0. Problem Zero: Read the section and make your own summary of the material. 1. True/False: Determine whether each of the statements that follow is true or false. If a statement is true, explain why. If a statement is false, provide a counterexample. (a) True or False: Functions are the same as equations. (b) True or False: The domain of every function is a subset of R.

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