Question

at what point is this function continuous, y=lx-1l+sin x, the answer is all X's, is this because of the abslt value? (l_l this means abslt value)

Answer 1

t would be continuous without the absolute value as well
it is only going to be discontinuous if it is either a 'step function', if the formula allows for division by zero, or a negative square root.
none of that is the case here

Answer 2

polynomials are continuous functions(except of course you have a fraction) and trigonometric functions(except tan and cotan) are also continuous so their sum is also continuous