The end behavior of a function describes how the function behaves as x approaches positive or negative infinity. To determine the end behavior of f(x) = 1 - 3x, we can look at the leading term, which is -3x.
As x becomes very large (either positive or negative), the value of -3x becomes very large in the opposite direction. That is, as x approaches positive infinity, -3x approaches negative infinity, and as x approaches negative infinity, -3x approaches positive infinity.
Since the constant term 1 does not have any effect on the end behavior, we can conclude that the function f(x) = 1 - 3x decreases without bound as x approaches positive infinity and increases without bound as x approaches negative infinity.
In other words, the end behavior of f(x) = 1 - 3x can be described as:
As x → ∞, f(x) → -∞
As x → -∞, f(x) → +∞