Graph the Function and Analyze It for Domain, Range, Continuity$$f ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }$$

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The Answer is $The domain is all real numbers, and the range is ( 0,4 ) . The function is continuous and decreasing on its domain. The graph is symmetric about \left( \ln \frac { 1 } { 3 } , 2 \right) , but neither even nor odd. It is bounded below and above. There are no local extrema. The horizontal asymptotes are y = 0 and y = 4 . The end behavior is described by \lim _ { x \rightarrow \infty } f ( x ) = 4 and \lim _ { x \rightarrow\infty } f ( x ) = 0 .$ The domain is all real numbers, and the range is

( 0,4 )

. The function is continuous and decreasing on its domain. The graph is symmetric about

\left( \ln \frac { 1 } { 3 } , 2 \right)

, but neither even nor odd. It is bounded below and above. There are no local extrema. The horizontal asymptotes are

y = 0

and

y = 4

. The end behavior is described by

\lim _ { x \rightarrow \infty } f ( x ) = 4

and

\lim _ { x \rightarrow\infty } f ( x ) = 0

.

Graph the Function and Analyze It for Domain, Range, Continuity $f ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }$

Definitions:

Graph the Function and Analyze It for Domain, Range, Continuity f(x)=41+3exf ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }f(x)=1+3ex4​

Definitions:

Graph the Function and Analyze It for Domain, Range, Continuity $f ( x ) = \frac { 4 } { 1 + 3 e ^ { x } }$