Better way to find function

To whom it may concern,

1. I would like to know if there is a command in R to choose a function for 
a given dataset. I am facing a difficult question about how to fit the data 
[ please attachment ]

2. Are there any function that will allow users to do the piecewise 
regression?

If not, is it going to be provide in the new updated version? What I am 
using is the piecewise logistic regression, but it doesn't have a continuous 
function though. I hope that R would have a specific command to do the 
piecewise (non)linear regression.

I would apprecaite your suggestion.

Sincerely yours,

Nhum

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