State the domain and range of the function.
-$$f ( x ) = e ^ { - x } + 1$$
A) domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$
B) domain: $( - \infty , \infty )$; range: $( - \infty , 1 )$
C) domain: $( - \infty , \infty )$; range: $( - \infty , - 1 ]$
D) domain: $( - \infty , \infty )$; range: $( 1 , \infty )$

Question

Quizplus · Accepted Answer

The domain of $f(x) = e^{-x} + 1$ is all real numbers because there are no restrictions on $x$ for the exponential function, hence $(- \infty, \infty)$. The range is $(1, \infty)$ because $e^{-x}$ is always positive, and adding 1 shifts the minimum value to 1, but it never includes 1 itself and can grow indefinitely large as $x$ becomes more negative.

State the Domain and Range of the Function f(x)=e−x+1f ( x ) = e ^ { - x } + 1f(x)=e−x+1

State the Domain and Range of the Function $f ( x ) = e ^ { - x } + 1$