I would like to use a software where you can sketch in the (x,y)-plane as follows:
you can click on the x-axis to place named interval endpoints such as a, b, c, d, etc…
you can define functions on those intervals by clicking on the intervals and entering the function formula for that interval
You may use the values a, b, c, d, from the endpoints in the formulas for the functions as variables.
You can gather the various functions on the intervals into one or more named functions.
You can define more than one function per interval.
You select the start endpoint and end endpoint of each function part and move the endpoints around by dragging them. The function drawn adjusts accordingly.
There may be other endpoints, for instance, belonging to other functions, between the start interval and the end interval of each function part.
You can also define (each function has a function color), composite functions (such as the sum or other composition of functions to display on the graph).
You can define sequences of functions to be shown in one color.
You can attach text notes to each interval.
Thank you for your support.