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chapter 1 37 - SECTION 1.5 EXPONENTIAL FUNCTIONS 37 3 All...

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Unformatted text preview: SECTION 1.5 EXPONENTIAL FUNCTIONS 37 3. All of these graphs approach 0 as an —> woo. all of them pass 5 y : 20‘ y = 5‘ y : 6‘ through the point (0, 1). and all of them are increasing and y=2“ approach 00 as a: —> 00. The larger the base. the faster the function increases for w > 0. and the faster it approaches 0 as Ifl—OO. 4. The graph of e” is the reflection of the graph of e“E about the y—axis, and the graph of 8’m is the reflection of that of 8m about the y—axis. The graph of 8" increases more quickly than that of em for a: > O, and approaches 0 faster as $—>—OO. 5. The functions with bases greater than 1 (31 and 10’”) are increasing. while those with bases less than 1 [6V and (710)? are decreasing. The graph of (am is the reflection of that of 3“: about the y—axis. and the graph of (1%):6 is the reflection of that of 10‘“ about the y—axis. The graph of 10“0 increases more quickly than that of 3x for :r > 0. and approaches 0 faster as a: —> —oo. 6. Each of the graphs approaches 00 as m —> —00. and each approaches 0 as :c —> 00. The smaller the base. the faster the function grows as as —+ —00, and the faster it approaches 0 as a: —> 00. y : 0.6‘ y 2 0.93 g _2 —0. 2 7. We start with the graph of y 2 4”” (Figure 3) 8. We start with the graph of y : 4m (Figure 3) and and then shift 3 units downward. This shift then shift 3 units to the right. There is a horizontal doesn‘t affect the domain, but the range of asymptote of y : 0_ y : 4z — 3 is (—3. oo) . There is a horizontal .v asymptote of y : —3. y y:¥ y=¥ ...
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