1. Trig graphs

Hello!
Hope someone can help with a bit of confusion i have!?

Im happy with sketching trig graphs generally but this question caught me out and i cant get my head around it!!....

"Sketch the graph of y = 1 + 3cosec2x". I thought that was simply the graph of y = cosec x stretched with scale factor 1/2 and 3 in the x and y direction respectively followed by a translation of vector (0, 1). This is where i went wrong, i drew my graph with the translation of 1 unit in the y direction when actually the stretch in the y direction had moved the vertexes of the upper parbolas a further 3 units up.

Why does a stretch in the y direction on this graph expand the series of parbolas away for the x axis thus moving the vertexes when the same transformation when applied to a single parbola ie y = 3(-x^2) does not move the location of the vertex?

Hope that makes sense!

Thanks for any help in advance.

2. If the function that the coefficient multiplies is anything other than zero, it will move away from the x axis. The vertex in x^2 is the same as 3(x^2) because 3 times 0 = 0. CSC pi/2 = 1. 3*1 = 3

3. Hello,
Thanks a lot, just had an experiment on my calculator! seems a bit clearer now but we shall see!