Parametric equations

https://www.quora.com/profile/Bravewarrior/p-147225613
Here is the question and its solution.Can anyone please explain the solution to part a? Thanks!

What is the range of y(t)? So if the horizontal line y=k intersects it, what range can k be?

For y(t) the range would be -1<y<1 and I guess if y=k intersects it then it becomes k=cos2t+1 but how would the horizontal line affect the range?

cos(2t) has a range -1 to 1, but
cos(2t) + 1 has a range 0 to 2

So if the horizontal line y=k intersects the curve, then k must have the same range 0 to 2 as the horizontal line y=3 say would be too high and the horizontal line y=-1 would be too low.