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Practical Algebra (Revised) Prepared for the Use of the Midshipmen at the United States Naval Academy

Practical Algebra (Revised) Prepared for the Use of the Midshipmen at the United States Naval Academy


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1910 Excerpt: ... or of (x + a)2, a being any given number. For instance, suppose we should construct the graph of (x2 + l) independently. For any value of x, the point representing (a + 1) would be one unit higher than the point representing x2; thus the graph of (z2 + l) would be the graph of x2 raised one unit. We can, however, get the same effect more easily by leaving the graph where it is and lowering the rr-axis one unit. In the same way, the graph of (x2--2) can be obtained from the graph of x2 by raising the z-axis two units. Again, suppose we should construct the graph of (z+1)2; in the table of values of x and (rr + 1)2, we should have the same set of values for (z+1)2 that we had for x2, except that the corresponding value of x would be one less. This means that the graph of (x+1)2 is the graph of x2 shifted one unit to the left, or is the graph of x2 with the y-axis shifted one unit to the right. In the same way, the graph of (x--2)2 can be obtained from the graph of x2 by shifting the -/-axis two units to the left. These considerations are perfectly general, and may be applied to any function: The graph of f(x) +a can be obtained from the graph of f(x) by shifting the x-axis a units downward; and The graph of f(x + a) can be obtained from the graph of f(x) by shifting the y-axis a units to the right. If a is negative, the shift is in the opposite direction. Examples. Draw the graphs of the following functions: 1. z2-3. 2. 2x2 + l. 3.-$x-. 4. x1. 5.-2x2. 6. x2 + x3. 7. x-and 2x + 3 on the same axes. How do the graphs show the values of x for which these two functions are equal? 8. 3? and 2x--l on the same axes. How do the graphs show the values of x for which x3--2x +1 = 0? 83. Slope of the Graph.--The steepness or slope of a graph at any point, which is t...


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Product Details
  • ISBN-13: 9781236230737
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 34
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1236230736
  • Publisher Date: 01 May 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 82 gr

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