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

Sep 7, 2014

The domain of the sine function is all Real numbers, or $\left(\setminus \infty , \setminus \infty\right)$.

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 $\left[- 1 , 1\right]$.

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].