Final answer:
The function f(x) = |2x + 1| + |x| - x does not have vertical asymptotes, because absolute value functions are continuous and do not approach infinity for any finite value of x, which is a requirement for a vertical asymptote.
Step-by-step explanation:
The function f(x) = |2x + 1| + |x| - x does not have vertical asymptotes. A vertical asymptote occurs where a function approaches infinity as the input approaches a certain value. However, due to the properties of absolute value functions, f(x) will be continuous and will never approach infinity for any finite value of x. Therefore, vertical asymptotes are not a characteristic of this function.
Looking at the given function, we can analyze it piece by piece. The term |2x + 1| represents the absolute value of 2x + 1, which is always nonnegative. The term |x| is the absolute value of x and is also always nonnegative. Subtracting x from the sum of these absolute values may create points where the function has a value of zero, but it will not create vertical asymptotes.