Final answer:
For the function f(x) = (x - 6)² + 2, as x approaches negative infinity, the expression (x - 6)² becomes a large positive number, which means f(x) approaches positive infinity. Therefore, the answer is option a. f(x) approaches positive infinity.
Step-by-step explanation:
The given function is f(x) = (x - 6)² + 2. To determine the end behavior as x approaches negative infinity, we look at the leading term of the polynomial function.
As x becomes very large negatively (x approaches negative infinity), the term (x - 6)² will also approach positive infinity since any real number squared is non-negative, and therefore large negative inputs lead to large positive outputs.
Additionally, when this large positive number is added to 2, the result is still approaching positive infinity. Therefore, the correct choice for the end behavior is (a) f(x) approaches positive infinity.
The given function is f(x) = (x - 6)² + 2. The end behavior as x approaches negative infinity can be determined by looking at the leading term of the function.
In this case, the leading term is (x - 6)², which is a quadratic term. When x approaches negative infinity, the quadratic term becomes infinitely large and positive. Therefore, the answer is option a. f(x) approaches positive infinity.