15_Cal_Solution of Calculus_6e

# 15_Cal_Solution of Calculus_6e - C01S02.039 Note that f...

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Unformatted text preview: C01S02.039: Note that f ( x ) &amp;gt; 0 for all x other than x = 1, where f is not defined. If | x | is large, then f ( x ) is near zero, so the graph of f almost coincides with the x-axis for such x . If x is very close to 1, then f ( x ) is the reciprocal of a very small positive number, hence f ( x ) is large positive. So for such x , the graph of f ( x ) almost coincides with the upper half of the vertical line x = 1. The only intercept is (0 , 1). C01S02.040: Note first that f ( x ) is undefined at x = 0. To handle the absolute value symbol, we look at two cases: If x &amp;gt; 0, then f ( x ) = 1; if x &amp;lt; 0, then f ( x ) = − 1. So the graph of f consists of the part of the horizontal line y = 1 for which x &amp;gt; 0, together with the part of the horizontal line y = − 1 for which x &amp;lt; 0. C01S02.041: Note that f ( x ) is undefined when 2 x + 3 = 0; that is, when x = − 3 2 . If x is large positive, then f ( x ) is positive and close to zero, so the graph of f is slightly above the x-axis and almost coincides with the x-axis. If x is large negative, then...
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