Is the function given by, f(x)={3x-2 if x≤3 , 10-x if x> 3} continuous at x = 3?

yes

This is a piecewise-defined function because it is defined by two or more equations over a specified domain is. The graph of this function is shown below. So this functions is continuous because its graph is a single unbroken curve. So the function is defined be the line 3x - 2 when x = 3 and the output here is y = 7

the reason why your question keeps getting deleted because this is not a school related question : )

i will answer your question though.

i never tried church's