Graph the function on your calculator to determine the domain and range from the graph.
-$$g ( x ) = \frac { 1 } { 1 + e ^ { - x } } - 3$$
A) Domain: $( - \infty , \infty )$; range: $( - 3 , - 2 )$
B) Domain: $( - \infty , \infty )$; range: $( - \infty , - 2 ]$
C) Domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$
D) Domain: $( 0 , \infty )$; range: $[ - 3 , - 2 ]$

Question

Quizplus · Accepted Answer

The function $g(x) = \frac{1}{1 + e^{-x}} - 3$ is defined for all real numbers, giving it a domain of $(-\infty, \infty)$. As $x$ approaches $-\infty$, $g(x)$ approaches $-3$, and as $x$ approaches $\infty$, $g(x)$ approaches $-2$, but never reaches these values, making the range $(-3, -2)$.

Graph the Function on Your Calculator to Determine the Domain g(x)=11+e−x−3g ( x ) = \frac { 1 } { 1 + e ^ { - x } } - 3g(x)=1+e−x1​−3

Graph the Function on Your Calculator to Determine the Domain $g ( x ) = \frac { 1 } { 1 + e ^ { - x } } - 3$