The cos family function is even. In the first picture it is the maximum (0,1). It shows two periods and the range is -1<x<equal too 1. It has the same repeated x factor. It also shows that the cosine curve is symmetric to the y-axis. The second picture Y=5Cos(x), shows the amplitude and the amplitude for cosine starts on the that specific number. The range is -5<x<equal too 5. The third picture shows the period shift. Y=cos(5x),Its range is also (-1,1). The period shift allows it too shrink or lengthen. The 4th picture Y=cos(x-5), horizontal shift. Its shift moves it to the left. The horizontal shift allows the graph to move left or right. The 5th picture,Y=5+cos(x), shows the vertical shift. This shift allows it to move up and down. The shift has moved up in the picture. +/- is what tells you which way to move.The range is still the same.The amplitude is the only thing that can change your range.