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Asymptote
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=== Transformations of known functions === If a known function has an asymptote (such as ''y''=0 for ''f''(x)=''e''<sup>''x''</sup>), then the translations of it also have an asymptote. * If ''x''=''a'' is a vertical asymptote of ''f''(''x''), then ''x''=''a''+''h'' is a vertical asymptote of ''f''(''x''-''h'') * If ''y''=''c'' is a horizontal asymptote of ''f''(''x''), then ''y''=''c''+''k'' is a horizontal asymptote of ''f''(''x'')+''k'' If a known function has an asymptote, then the [[Homothetic transformation|scaling]] of the function also have an asymptote. * If ''y''=''ax''+''b'' is an asymptote of ''f''(''x''), then ''y''=''cax''+''cb'' is an asymptote of ''cf''(''x'') For example, ''f''(''x'')=''e''<sup>''x''-1</sup>+2 has horizontal asymptote ''y''=0+2=2, and no vertical or oblique asymptotes.
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