State the domain and range of the function.
-$$f ( x ) = - 6 e ^ { - x } + 1$$
A) domain: $( - \infty , \infty ) \cup ( - \infty , \infty )$; range: $( - \infty , 1 )$
B) domain: $( - \infty , \infty )$; range: $( - \infty , \infty )$
C) domain: $( - \infty , \infty )$; range: $( - \infty , 1 ]$
D) domain: $( - \infty , \infty )$; range: $( - \infty , 1 )$

Question

Quizplus · Accepted Answer

The function has no restrictions on the domain as it is defined for all real numbers. However, the range is restricted as the exponential term is always decreasing and the constant term only shifts the graph up or down. Therefore, the maximum value of the function is 1, and it approaches negative infinity as x approaches infinity. Thus, the range is $(-\infty,1)$. The correct choice is D.

State the Domain and Range of the Function f(x)=−6e−x+1f ( x ) = - 6 e ^ { - x } + 1f(x)=−6e−x+1

State the Domain and Range of the Function $f ( x ) = - 6 e ^ { - x } + 1$