Question: Linear spline set constant endpoints

I have a set of points. I want to make a linear spline of that points and plot the resulting function:


However I need the function to define constant y endpoint values where x is out of points_x range (i.e. first-derivation is zero where x is out of points_x range). Endpoint options does not work for me.

             constant1   x < xmin
function :=  ..
             constant2   otherwise

How can I define spline function like this?

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