# Question #d7048

Apr 2, 2017

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= $\frac{\pi}{4}$ 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= $\frac{3 \pi}{4}$, 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.