By Vasile Cirtoaje
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Extra info for Algebraic inequalities
Explain how each graph is obtained from the graph of y f ͑x͒. (a) y f ͑x͒ ϩ 8 (c) y 8 f ͑x͒ (e) y Ϫf ͑x͒ Ϫ 1 (b) y f ͑x ϩ 8͒ (d) y f ͑8x͒ (f) y 8 f ( 18 x) 22. (a) How is the graph of y 2 sin x related to the graph of y sin x ? Use your answer and Figure 18(a) to sketch the graph of y 2 sin x. (b) How is the graph of y 1 ϩ sx related to the graph of y sx ? Use your answer and Figure 17(a) to sketch the graph of y 1 ϩ sx . 23–36 ■ Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.
The table of values shown in the margin is the most convenient representation for this function, though it is possible to sketch a graph (see Example 6). D. The graph shown in Figure 1 is the most natural representation of the vertical acceleration function a͑t͒. It’s true that a table of values could be compiled, and it is even possible to devise an approximate formula. But everything a geologist needs to know—amplitudes and patterns—can be seen easily from the graph. ) In the next example we sketch the graph of a function that is deﬁned verbally.
68 и и и и и и The function P is typical of the functions that arise whenever we attempt to apply calculus to the real world. We start with a verbal description of a function. Then we may be able to construct a table of values of the function, perhaps from instrument readings in a scientiﬁc experiment. Even though we don’t have complete knowledge of the values of the function, we will see throughout the book that it is still possible to perform the operations of calculus on such a function. C. Again the function is described in words: Let C͑w͒ be the cost of mailing a large envelope with weight w.
Algebraic inequalities by Vasile Cirtoaje