which function is not graphed correctly?\no a. y = sin x\no b. y = cos x\no c. y = cot x\no d. y = tan x

Explanation:

Step1: Recall properties of trig - functions

The function (y = \sin x) has a range of ([- 1,1]), period (T = 2\pi), and passes through the origin ((0,0)). The graph in option A is a correct graph of (y=\sin x).

Step2: Recall properties of cosine function

The function (y=\cos x) has a range of ([-1,1]), period (T = 2\pi), and (y(0)=1). The graph in option B is a correct graph of (y = \cos x).

Step3: Recall properties of cotangent function

The function (y=\cot x=\frac{\cos x}{\sin x}) has vertical asymptotes at (x = n\pi), (n\in\mathbb{Z}), and is zero at (x=(n +\frac{1}{2})\pi), (n\in\mathbb{Z}). The graph in option C is a correct graph of (y=\cot x).

Step4: Recall properties of tangent function

The function (y = \tan x=\frac{\sin x}{\cos x}) has vertical asymptotes at (x=(n+\frac{1}{2})\pi), (n\in\mathbb{Z}), and passes through the origin ((0,0)). The graph in option D has incorrect vertical - asymptote positions. The vertical asymptotes of (y = \tan x) should be at (x=\frac{\pi}{2}+n\pi), (n\in\mathbb{Z}), but the graph in option D has them at (x = n\pi) which is wrong.

Answer:

D. (y = \tan x)