State the domain and range of the function.
-$$f ( x ) = 2 ^ { - x } + 2$$
A) domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , 2 )$
B) domain: $( - \infty , \infty )$; range: $( - \infty , 2 )$
C) domain: $( - \infty , \infty )$; range: $( - \infty , 2 ]$
D) domain: $( - \infty , \infty )$; range: $( 2 , \infty )$

Question

Quizplus · Accepted Answer

The function $f(x) = 2^{-x} + 2$ is defined for all real numbers, hence its domain is $(- \infty , \infty )$. As $x$ approaches infinity, $2^{-x}$ approaches 0, making the function approach 2. As $x$ approaches negative infinity, $2^{-x}$ grows without bound, making the function's value increase indefinitely. Therefore, the range is $(2, \infty)$.

State the Domain and Range of the Function f(x)=2−x+2f ( x ) = 2 ^ { - x } + 2f(x)=2−x+2

State the Domain and Range of the Function $f ( x ) = 2 ^ { - x } + 2$