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 a variety of purposes designed to inspire scholars with various pursuits, transparent examples detailing very important mathematical techniques, and an unlimited selection of workouts applicable for college kids with disparate ability units, this primary version is ideal for college kids who have to the best way to observe calculus suggestions instead of mirror the formal proofs at the back of the options. Early insurance of exponential and logarithmic features makes it possible for the inclusion of many attention-grabbing functions during the textual content. on hand with quite a number supplementations together with improved WebAssign, short utilized CALCULUS makes calculus approachable so any scholar can comprehend the ideas and be triumphant within the path.

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**Example text**

If we compare the graphs of y f ͑x͒ and y Ϫf ͑x͒ in Figure 6, the graph of y Ϫf ͑x͒ is the graph of y f ͑x͒ but flipped upside down. 2 ■ Combining and Transforming Functions 23 x-axis. If you compare the graph of y f ͑x͒ with the graph of y f ͑Ϫx͒ in Figure 6, you’ll notice that this time the x-values are made opposite, so the graph appears reflected about the y-axis. ■ Vertical and Horizontal Reflections reflection of the graph of y f ͑x͒ equation y Ϫf ͑x͒ y f ͑Ϫx͒ reflect about the x-axis reflect about the y-axis Figure 7 illustrates several combinations of various transformations.

This enables us to make the rough sketch of T as a function of t in Figure 9. 1 T t 0 F IGURE 9 ■ A more accurate graph of the function in Example 3 could be obtained by using a thermometer to measure the temperature of the water at 10-second intervals. In general, researchers collect experimental data and use them to sketch the graphs of functions, as the next example illustrates. 0 The data shown in the margin give weekly sales figures for a video game shortly after its release. Let N͑t͒ be the number of copies sold, in thousands, during the week ending t weeks after the game’s release.

B) Complete the graph of f if it is known that f is odd. y 20 x x x x x x 12 x _5 0 x 5 x Taxi fares A taxi company charges two dollars for the first mile (or part of a mile) and 20 cents for each succeeding tenth of a mile (or part). Express the cost C, in dollars, of a ride as a function of the distance x traveled, in miles, for 0 Ͻ x Ͻ 2, and sketch the graph of this function. Income tax In a certain country, income tax is assessed as follows. There is no tax on income up to $10,000. Any income beyond $10,000 is taxed at a rate of 10%, up to an income of $20,000.