Non-parametric methods do not explicitly assume a parametric form for the hypothesis function f(X), and thereby provide an alternative and more flexible approach for performing regression or classification. In case of regression, the simplest and best-known non-parametric method is probably K -nearest neighbors regression (KNN regression). 

On the contrary, parametric methods involve a two-step model-based approach 

First, making an assumption about the functional form, or shape, of f(X); e.g. f(X) is linear in X 

After a model has been selected, using a procedure on the training data to fit  or train the model; e.g. in case f(X) is linear in X we need to estimate the linear coefficients of f(X)

Generally speaking, the parametric approach will outperform the nonparametric approach if the parametric form that has been selected is close to the true form of f(X). E.g. in case of a regression problem if the true relationship is linear, it is hard for a non-parametric approach to compete with a linear regression as a non-parametric approach incurs a cost in variance that is not offset by a reduction in bias. On the other hand, if the true relationship is not linear, a non-parametric approach such as KNN can be superior than linear regression.  

As a general rule, parametric methods will tend to outperform non-parametric approaches when there is a small number of observations per predictor. 

Also, non-parametric methods such as KNN can still give poor results if the level of smoothness is not chosen correctly, e.g. in case of KNN regression the number (k) of nearest neighbors. 

So, coming to your question, it is not only the train data range of the single predictor  (2.5-7.5 in your example) that matters in order to choose between a non-parametric approach and a parametric approach but how close is the true form of f(X) with the parametric model you choose. If you don't know such a true form of f(X) or it is far enough from any parametric model you are evaluating, it is not uncommon that a nonparametric approach will give you better results.  

The simple answer is 'no', you cannot extrapolate.   :)

Agree with all, basically no.

I try to keep this in simple terms. :)

ANN can only produce result in pre determined output range, from pre determined input range, in which can be as long as you want (before fuzzy-fied to 0 to 1 range, off course), but

"completeness" of training data, whether it has sample to much possible combi, is needed to ensure accuracy of ANN output. :)