consider-the-function-fx5exfleftxright5e-x-what-is-the-end-behavior-of-this-func

Question

Consider the transcendental function $f\left(x\right)=5e^{-x}$ . 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

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

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

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

Answer

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

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

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

Answer

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

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

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

Answer

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

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

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

Consider the transcendental function $f\left(x\right)=5e^{-x}$ . 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.