What is the range of [tex]$f(x)=-3^x-1$[/tex]?
A. the set of real numbers greater than 0
B. the set of real numbers less than -1
C. the set of real numbers less than 0
D. the set of real numbers greater than -1

To find the range of the function f(x) = -3^x - 1, we first need to determine the behavior of the function as x approaches negative infinity and positive infinity.

As x approaches negative infinity:

Since 3 raised to any negative number is a positive number, and the exponent keeps decreasing as x approaches negative infinity, the term -3^x goes to 0.

As x approaches positive infinity:

Since 3 raised to any positive number is a positive number, and the exponent keeps increasing as x approaches positive infinity, the term -3^x goes to infinity.

Therefore:

The range of the function: f(x) = -3^x - 1, is:

A. the set of real numbers greater than 0

Explanation: For any real number x greater than 0, the function f(x) will be greater than -1, and the term -3^x will be a positive number. Thus, the resulting value of the function will be a positive number, which is in the set of real numbers greater than 0.