By Wolfgang Walter
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Extra info for Analysis 2 (Springer-Lehrbuch)
Indd 17 7/21/16 4:31 PM R-18 Chapter R Algebra Reference –1 – 3 0 5 The solution y Ú -3 / 5 in Example 1 represents an interval on the number line. Interval notation often is used for writing intervals. With interval notation, y Ú -3 / 5 is written as 3-3 / 5, ∞2. This is an example of a half-open interval, since one endpoint, -3 / 5, is included. The open interval 12, 52 corresponds to 2 6 x 6 5, with neither endpoint included. The closed interval 32, 54 includes both endpoints and corresponds to 2 … x … 5.
When we do, it is important to be consistent. S. 1% in 2012. Source: Centers for Disease Control and Prevention. (a) Find the equation describing this linear relationship. Solution Let t represent time in years, with t = 0 representing 2000. With this rescaling, the year 2005 corresponds to t = 5 and the year 2012 corresponds to t = 12. Let y represent the percentage of the population who smoke. 12. 4. 4% per year. 92, gives the required equation. 9 to both sides. 12 and found the same answer. 1, which agrees with the y-value at t = 12.
To see how slope is defined, look at the line in Figure 3. The line passes through the points 1x 1 , y1 2 = 1-3, 52 and 1x 2 , y2 2 = 12, -42. The difference in the two x-values, y ∆x = 2 – (–3) =5 ∆y = –4 – 5 = –9 x x2 - x1 = 2 - 1-32 = 5 in this example, is called the change in x. The symbol ∆x (read “delta x”) is used to represent the change in x. In the same way, ∆y represents the change in y. In our example, (2, –4) Figure 3 a Quadrant IV Figure 1 (–3, 5) x-intercept is a. b ∆y = y2 - y1 = -4 - 5 = -9.
Analysis 2 (Springer-Lehrbuch) by Wolfgang Walter