What function is graphed below? y=cot(x-(pi )/(4)) y=tan(x-(pi )/(4))

To determine which function is graphed, let's analyze the behavior of the two given functions and compare them to the description of the graph provided in the picture details.1. \(y=\cot \left(x-\frac{\pi}{4}\right)\)The cotangent function, \(\cot(x)\), has the following properties:- It is undefined at \(x = k\pi\) where \(k\) is an integer, because these are the zeros of the tangent function.- It has vertical asymptotes at \(x = k\pi\).- It is positive in the first and third quadrants, and negative in the second and fourth quadrants.- It decreases monotonically between its vertical asymptotes.For \(y=\cot \left(x-\frac{\pi}{4}\right)\), the graph of the cotangent function is shifted to the right by \(\frac{\pi}{4}\) units. This means that the vertical asymptotes will occur at \(x = \frac{\pi}{4} + k\pi\).2. \(y=\tan \left(x-\frac{\pi}{4}\right)\)The tangent function, \(\tan(x)\), has the following properties:- It is undefined at \(x = \frac{\pi}{2} + k\pi\) where \(k\) is an integer, because these are the points where the cosine function is zero, and tangent is sine over cosine.- It has vertical asymptotes at \(x = \frac{\pi}{2} + k\pi\).- It is positive in the first and third quadrants, and negative in the second and fourth quadrants.- It increases monotonically between its vertical asymptotes.For \(y=\tan \left(x-\frac{\pi}{4}\right)\), the graph of the tangent function is shifted to the right by \(\frac{\pi}{4}\) units. This means that the vertical asymptotes will occur at \(x = \frac{\pi}{4} + \frac{\pi}{2} + k\pi\) or simplified \(x = \frac{3\pi}{4} + k\pi\).Now, let's compare these properties to the graph description:- The function decreases monotonically in the interval (-∞, -1).- The function passes through the point (-2, 0).- As x approaches -∞, y approaches 0; as x approaches -1, y approaches -∞.The description suggests that the function has a vertical asymptote at x = -1 and passes through the point (-2, 0). The cotangent function has a decreasing behavior between its vertical asymptotes, which matches the description of the graph. The tangent function, on the other hand, increases monotonically between its vertical asymptotes, which does not match the description.Given that the function in the description decreases monotonically and has a vertical asymptote at x = -1, the correct function that matches this behavior is:\(y=\cot \left(x-\frac{\pi}{4}\right)\)Therefore, the function graphed is \(y=\cot \left(x-\frac{\pi}{4}\right)\). Mark this and return.