By James Stewart, Daniel Clegg

New from James Stewart and Daniel Clegg, short utilized CALCULUS takes an intuitive, much less formal method of calculus with out sacrificing the mathematical integrity. that includes quite a lot of functions designed to inspire scholars with various pursuits, transparent examples detailing vital mathematical tactics, and an enormous selection of routines applicable for college kids with disparate ability units, this primary version is ideal for college kids who have to observe calculus recommendations instead of mirror the formal proofs at the back of the innovations. Early assurance of exponential and logarithmic features permits the inclusion of many fascinating purposes during the textual content. to be had with various vitamins together with greater WebAssign, short utilized CALCULUS makes calculus approachable so any pupil can comprehend the thoughts and succeed within the direction.

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If f and t are both even functions and h͑x͒ f ͑x͒ ϩ t͑x͒, is h even? If f and t are both odd functions, is h odd? What if f is even and t is odd? Justify your answers. © Brooks Cole / Cengage Learning 64. Window area A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the window is 30 ft, express the area A of the window as a function of the width x of the window. 2 Combining and Transforming Functions In this section we form new functions by combining existing functions in various ways.

To see why this is the case, note that if t͑x͒ f ͑x ϩ 3͒, then t͑1͒ f ͑1 ϩ 3͒ f ͑4͒, so the output corresponding to x 4 in the graph of f is plotted with x 1 in the graph of t, 3 units to the left. Similarly, y f ͑x Ϫ 3͒ shifts the graph of f to the right 3 units. ■ Vertical and Horizontal Shifts Suppose c is a positive number. translation of the graph of y f ͑x͒ equation this is shift c units upward shift c units downward shift c units to the right shift c units to the left y y y y f ͑x͒ ϩ c f ͑x͒ Ϫ c f ͑x Ϫ c͒ f ͑x ϩ c͒ 01_ptg01_hr_022-031_23825_ch01_ptg01_hr_022-031 6/21/11 10:30 AM Page 22 CHAPTER 1 ■ Functions and Models We can also stretch (or compress) graphs.

H) Shrink vertically by a factor of 3. 34. Explain how the following graphs are obtained from the graph of y f ͑x͒. (a) y 5 f ͑x͒ (b) y f ͑x Ϫ 5͒ (c) y Ϫf ͑x͒ (d) y Ϫ5 f ͑x͒ (e) y f ͑5x͒ (f) y 5 f ͑x͒ Ϫ 3 35. The graph of y f ͑x͒ is given. Match each equation with its graph and give reasons for your choices. (a) y f ͑x Ϫ 4͒ (b) y f ͑x͒ ϩ 3 1 (c) y 3 f ͑x͒ (d) y Ϫf ͑x ϩ 4͒ (e) y 2 f ͑x ϩ 6͒ y @ 6 3 f ! 2 Combining and Transforming Functions 27 48. Given the graph of y x 2 as shown in Figure 9, use transformations to create a function whose graph is as shown.