Final answer:
The function f(x)=|x+2| has no vertical or horizontal asymptotes, as the values of the function do not approach a specific value but rather increase linearly due to the nature of the absolute value.
Step-by-step explanation:
For the function f(x)=|x+2|, we are examining the type of asymptotes that are present in the graph of the function. A vertical asymptote occurs when the graph of a function approaches a vertical line x=a as x approaches a from the left or the right and the function values increase or decrease without bound. However, because the function given is an absolute value function, it will not have any vertical asymptotes. As the function approaches infinity, the absolute value function will continue to grow in a linear fashion, and there will be no value of x at which the function is undefined or increases/decreases without bound. A horizontal asymptote occurs when the values of a function approach a constant value as x approaches infinity or negative infinity. In the case of the absolute value function |x+2|, as x approaches infinity or negative infinity, the function value will continue to increase and not approach a horizontal line. Therefore, there are no horizontal asymptotes at y=0 or y=2 either.
The correct statement regarding the function f(x)=|x+2| is that it has no asymptote. As x increases or decreases without bound, the function does not approach any particular value, but rather keeps increasing in the positive direction due to the nature of the absolute value. This eliminates a vertical asymptote and horizontal asymptotes as possibilities for this function.