Final answer:
The function f(x) = 3x + 3 is increasing for all real numbers, because the slope is positive. Without specific intervals, we can state it is increasing everywhere in its domain.
Step-by-step explanation:
To answer the question about the largest interval of x-values where the function is increasing: First, looking at the function f(x) = -x + 4x + 3, we need to simplify it by combining like terms. The simplified form is f(x) = 3x + 3. Since the coefficient of x is positive, this linear function is increasing everywhere in its domain. However, if we are given certain intervals, we would identify within those intervals where it is increasing.
No specific intervals are given in the question's supporting information, but generally, the function f(x) = 3x + 3 is increasing for all real numbers because the slope (3) is positive. In the context of a continuous probability function or other specified intervals, we would need the specific interval limits to determine where the function is increasing within those bounds. The question about a horizontal line being a graph of f(x) is unrelated to the given function and likely a typo as mentioned.