Final answer:
The end behavior of the function g(x) = 4|x − 2| − 3 is such that as x approaches either positive or negative infinity, the function value increases without bound.
Step-by-step explanation:
The question is related to understanding the end behavior of the function g(x) = 4|x − 2| − 3. To determine the end behavior, we need to look at the values of g(x) as x approaches positive and negative infinity. The function g(x) is an absolute value function which is modified by a vertical shift and a multiplication factor.
Let's break it down into two cases based on the definition of the absolute value:
- For x − 2 ≥ 0 (i.e., x ≥ 2), the function is equivalent to g(x) = 4(x − 2) − 3, which is a linear function with a slope of 4. As x goes to positive infinity, so does g(x).
- For x − 2 < 0 (i.e., x < 2), the function is equivalent to g(x) = 4(2 − x) − 3, which is also a linear function but with a negative slope of −4. As x goes to negative infinity, g(x) goes to positive infinity.
Therefore, no matter which direction x approaches from, positive or negative infinity, the function g(x) will increase without bound.