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chapter 1 23 - SECTION 1.3 NEW FUNCTIONS FROM OLD FUNCTIONS...

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Unformatted text preview: SECTION 1.3 NEW FUNCTIONS FROM OLD FUNCTIONS C 23 28. The most important features of the given graph are the w—intercepts and the maximum and minimum points. The graph of y = 1 / f (x) has vertical asymptotes at the :c—values where there are m—intercepts on the graph of y = f (x) The maximum of 1 on the graph of y = f (ac) corresponds to a minimum of 1/1 = 1 on y = 1 / f (m) . Similarly, the minimum on the graph of y : f (as) corresponds to a maximum on the graph of y = 1 / f (av) . As the values of y get large (positively or negatively) on the graph of y = f (av), the values of 3/ get close to zero on the graph 0fy=1/f($)- l 7m? " 29. Assuming that successive horizontal and vertical gridlines are a unit apart, we can make a table of approximate values as follows. m 0 f(x) 2 1.7 1.3 g(:c) 2 2.7 3 f(a:) + 9(2) 4 4 4 4.3 Connecting the points (cc, f (ac) + g(a:)) with a smooth curve gives an approximation to the graph of f + 9. Extra points can be plotted between those listed above if necessary. 30. First note that the domain of f + g is the intersection of the domains of f and 9; that is, f + g is only defined where both f and g are defined. Taking the horizontal and vertical units of length to be the distances between successive vertical and horizontal gridlines, we can make a table of approximate values as follows: .7: —2 —1 0 1 flat) —1 2.2 2.0 2.4 9(2) 1 —1.3 —1.2 —0.6 f(:c) + g(2:) 0 0.9 0.8 1.8 ...
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