What is the range of f(x)=−3x−1?

Question

the set of real numbers less than 0

the set of real numbers greater than 0

the set of real numbers greater than −1

the set of real numbers less than −1 <my choice

Answer 1

as written, f(x) has a range of all real numbers.

Pick any value for f(x), and you can easily find an x to produce it. For example, suppose you want

f(x) = 11
-3x-1 = 11
-3x = 12
x = -4

So, you must have a typo. Your range of f < -1 could be produced with

f(x) = -3x^2 - 1
f(x) = -|3x| - 1
f(x) = -3^x - 1

Maybe that's what you meant.