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chapter 1 35

# chapter 1 35 - SECTION 1.4 GRAPHING CALCULATORS AND...

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Unformatted text preview: SECTION 1.4 GRAPHING CALCULATORS AND COMPUTERS Cl 35 (d) o The graphs of all functions of the form y = 1/23" pass through the point (1, l). o If n is even, the graph of the function is entirely above the x—axis. The graphs of 1 / at” for 71, even are similar to one another. 0 If n is odd, the function is positive for positive a: and negative for negative x. The graphs of 1 /x” for n odd are similar to one another. 0 As n increases, the graphs of 1 / m" approach 0 faster as at —) oo. 31. f(x) = \$4 + c212 + a3. Ifc < 0, there are three humps: two minimum points and a maximum point. These humps get ﬂatter as 0 increases, I‘k‘M 2.5 32. f (as) = \/ 1 + 0332. If c < 0, the function is only deﬁned on [—1/\/——c , 1 /\/—_c ], and its graph is the top half of an ellipse. If c : 0, the graph is the line y : 1. If c > 0, the graph is the top half of a hyperbola. As 0 approaches 0, these curves become ﬂatter and approach the line y = 1. am‘: —1—20 —025 until at c : 0 two of the humps disappear and there is only one _2 5 minimum point. This single hump then moves to the right and approaches the origin as c increases. 33. y = 737?". As 71 increases, the 4.5 600 maximum of the function moves further from the origin, and gets larger. Note, however, that regardless of n, the function approaches 0 as a: —> 00. K 0 /‘ _ 8 0 A 20 x 34. y = #2. The “bullet” becomes broader as 0 increases. 0.1 5 1 6 16 c — a: —4 35. y2 2 ca:3 + 1'2 If c < 0, the loop is to the right of the origin, and if c is positive. it is to the left. In both cases, the closer c is to 0, the larger the loop is. (In the limiting case, 0 = 0, the loop is “inﬁnite”, that is, it doesn’t close.) Also, the larger M is, the steeper the slope is on the loopless side of the origin. ...
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