Cotangent is similar to the graph of tangent and has a period of pi. The reciprocal is Y=cotx= (1/tanx). In this picture it shows two periods and the range is -infinity to infinity. The points on this graph is undefined and 0. The vertical asymptotes is x=npi. The next picture, Y=2cot(x), showing the amplitude. The amplitude is 2 and it starts the graph on the x-axis. The range is undefined. The next picture is Y=cot(2x), it shows the period shift. The period shift allows it become smaller. Each wave is on 1 of the x-axis and repeating on the y-axis. Y=cot(x-2) , the 4th picture is showing the horizontal shift with the range remaining the same. All it has done is move it to the left. The last picture shows the vertical shift. Y=2+ cot(x), the range is still the same moving it up 2. It starts the point at 2.