What is the range of f(x)=−3x−1?
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
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.
To determine the range of a function, we need to find all possible output values, also known as the y-values, of the function. In this case, we have the function f(x) = -3x - 1.
To find the range, we should consider the possible values that -3x - 1 can take. Let's analyze the expression -3x - 1:
If x is a very large positive number, then -3x will be a very large negative number, and when we subtract 1 from that, the result will still be a large negative number. So, as x gets larger and larger, the value of -3x - 1 decreases without bound. This means that the function doesn't have an upper limit.
As for the lower limit, we can also see that no matter how small x gets, -3x - 1 will always be greater than or equal to -1. Thus, the range of the function f(x) = -3x - 1 is all real numbers greater than or equal to -1.
Therefore, the correct answer is "the set of real numbers greater than or equal to -1."