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**Unformatted text preview: **7) Asymptotes: Lecture 25 8 Translations ex. Sketch each function: 1) f ( x ) = 3 x-1 2) f ( x ) = 3-( x +3)-2 Lecture 25 9 The Exponential Function with base e Consider the following table of values (p. 336): m (1 + 1 m ) m 10 2.59374 100 2.70481 1000 2.71692 10,000 2.71815 100,000 2.71827 1,000,000 2.71828 Lecture 25 10 The Base e Def. 1) 2) NOTE: e ≈ Def. the exponential function: Lecture 25 11 The graph of the exponential function : ex. Graph f ( x ) = e x . x y ex. Graph f ( x ) = e-x . Lecture 25 12 NOTE: 1) lim x →∞ e x 2) lim x →-∞ e x 3) lim x →∞ e-x 4) lim x →-∞ e-x Lecture 25 13 ex. Find each horizontal asymptote of the graph of a) f ( x ) = 1 e x-2 b) f ( x ) =-3 4 + e-x...

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