4.5.2 Properties of the tangent function

. . Properties of the tangent function From the graph of y = tan , we observe the following properties of tangent function. (i) The graph is not continuous and has discontinuity points at x ∈ π ,  . (ii) The partial graph is symmetric about the origin for − < < (iii) It has infinitely many vertical asymptotes x ∈ π ,  . (iv) The tangent function has neither maximum nor minimum. Remark (i) The graph of y bx goes through one complete cycle for < < b and its period is p b . (ii) For y bx , the asymptotes are the lines x b k ∈  . (iii) Since the tangent function has no maximum and no minimum value, the term amplitude for tan x cannot be defined. Fig. . − π − π − O = tan Inverse - - Inverse Trigonometric Functions