abelkoontz Posted January 17, 2017 Report Share Posted January 17, 2017 how to find the horizontal asymptote of f(x)=10e-0.201x+3?? why is it y=3 Reply Link to post Share on other sites More sharing options...
kw0573 Posted January 17, 2017 Report Share Posted January 17, 2017 Recall transformations of a function and that g(x) = e^x has a horizontal assymptote at y = 0. f(x) is g(x) vertically stretched by a factor of 10, horizontally stretched by a factor of 1/0.201, reflected across the y-axis, then translated 3 units up. As a result, the new horizontal asymptote is at y = 3, which is only affected by any vertical translation. In general, the horizontal asymptote(s) is/are y = limit f(x) as x--> +/- infinity. Since the limit in this case towards negative infinity does not exist, the only horizontal asymptote is the y = lim f(x) as x--> + inf = 3. Both ways are valid and both need some visualization of the function in question. Reply Link to post Share on other sites More sharing options...
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