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Question

Consider the transcendental function $f (x) = 5 e^{- x}$ . What is the end behavior of this function as $x$ approaches $\infty$ and $- \infty$ ? Sketch a graph of the function, showing asymptotes if they exist.

Accepted Answer

$\lim_{x \to \infty} 5 e^{- x} = 0$

$\lim_{x \to - \infty} 5 e^{- x} = \infty$

Graph of f(x)=5e^(-x) showing end behavior as x approaches ±∞.

Answer

$\lim_{x \to \infty} 5 e^{- x} = 0$ $negative 2$

$\lim_{x \to - \infty} 5 e^{- x} =$ $\infty$

Graph of f(x)=5e^(-x) illustrating limits as x approaches ±∞.

Answer

$\lim_{x \to \infty} 5 e^{- x} = 0$ $negative 2$

$\lim_{x \to - \infty} 5 e^{- x} =$ $0$

Graph of f(x)=5e^(-x) depicting asymptotic behavior as x approaches ±∞.

Answer

$\lim_{x \to \infty} 5 e^{- x} = 0$ $negative 2$

$\lim_{x \to - \infty} 5 e^{- x} =$ $0$

Graph of f(x)=5e^(-x) showing behavior as x approaches ±∞ with asymptotes.

Consider the transcendental function f(x)=5e−xf\(\left\)(x\(\right\))=5e^{-x}. What is the end behavior of this function as xx approaches ∞\(\infty\) and −∞-\(\infty\)? Sketch a graph of the function, showing asymptotes if they exist.

Consider the transcendental function $f (x) = 5 e^{- x}$ . What is the end behavior of this function as $x$ approaches $\infty$ and $- \infty$ ? Sketch a graph of the function, showing asymptotes if they exist.