State the domain and range of the function.
-$$f ( x ) = - 5 ^ { - x } - 4$$
A) domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$
B) domain: $( - \infty , \infty )$; range: $( - \infty , - 5 )$
C) domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , - 4 )$
D) domain: $( - \infty , \infty )$; range: $( - \infty , - 4 )$

Question

Quizplus · Accepted Answer

The function has a domain of all real numbers, as there are no restrictions on the input. The range, however, is limited by the fact that the exponential term approaches 0 as x approaches infinity and becomes increasingly negative as x approaches negative infinity. Therefore, the range is all real numbers less than or equal to -4, which is option D.

State the Domain and Range of the Function f(x)=−5−x−4f ( x ) = - 5 ^ { - x } - 4f(x)=−5−x−4

State the Domain and Range of the Function $f ( x ) = - 5 ^ { - x } - 4$