State the domain and range of the function.
-$$f ( x ) = 2 ^ { x } + 5$$
A) domain: $( - \infty , 0 ) \cup ( 0 , \infty )$; range: $( 5 , \infty )$
B) domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$
C) domain: $( - \infty , \infty )$; range: $[ 5 , \infty )$
D) domain: $( - \infty , \infty )$; range: $( 5 , \infty )$

Question

Quizplus · Accepted Answer

The function is defined for all real numbers, hence the domain is $(-\infty,\infty)$. As the base of the exponential function is 2, and 2 raised to any real number is positive, the range of the function is all positive real numbers plus 5, which is $(5,\infty)$. Therefore, the correct choice is (D).

State the Domain and Range of the Function f(x)=2x+5f ( x ) = 2 ^ { x } + 5f(x)=2x+5

State the Domain and Range of the Function $f ( x ) = 2 ^ { x } + 5$