Question

Question #d7048

Answer 1

Explained below

Explanation:

The graph of y= 3 cot x +2, can be drawn, first , by vertical stretch of the graph of y= cot x by a factor of 3 and then horizontal shift to the right by 2 units.
The vertical stretch has been explained in the attached figure. The red outlines are for the graph of cot x, with vertical asymptotes at x=0, `pi`, ... Now at point x= `pi/4` cot x =1. On vertical stretch this would shift to 3. This shift has been shown by a point circled in blue pen.

At point x=(pi/2), cot x =0, hence this point would remain where it is.

Next at point x= `(3pi)/4`, cot x =-1. On vertical stretch, this point would shift to -3. This point has also been shown circled in blue pen.

Asymptotes at x=0 and x= `pi` would remain same.

The vertical stretch of the graph of cot x, from x=0 to x=`pi` has been shown by the graph in blue pen.

Having stretched the graph, this can be shifted 2 units to the right to have the desired graph.