Final answer:
The end behavior of the function f(x) = 3 - 22/(x + 6) is that it approaches the horizontal asymptote y = 3 as x approaches both positive and negative infinity.
Step-by-step explanation:
To discuss the end behavior of the function f(x) = 3x - 4/(x + 6), which is also written as f(x) = 3 - 22/(x + 6), we first need to understand that end behavior describes how a function behaves as x approaches positive or negative infinity.
As x approaches positive infinity (x → ∞), the term -22/(x + 6) approaches zero since the denominator grows much larger than the numerator. Consequently, f(x) approaches the horizontal asymptote y = 3 because -22/(x + 6) becomes insignificant in impacting the function's value.
Similarly, as x approaches negative infinity (x → -∞), the term -22/(x + 6) also approaches zero, and thus the function again approaches the horizontal asymptote y = 3.
In summary, the end behavior of the function is such that f(x) approaches y = 3 as x approaches either positive or negative infinity.