Question

What is the domain of `y = 2sinx+ 1`?

Answer 1

The domain of the sine function is all Real numbers, or `(\infty,\infty)`.

That means that this function will continue to repeat its values infinitely to the left and right along the x-axis. (see graph)

It might be beneficial to talk about the range of this function. The normal sine function graph oscillates between -1 and 1. Written in interval notation, this would be `[-1,1]`.

This function, y = 2sin(x) + 1 has undergone a vertical stretch (multiplied by 2) as well as a vertical translation of up 1. Look at the graph to see the new minimum and maximum of -1 and 3. Thus, the range is [-1,3].