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.