The graph of y=tan[(1)/(4)(x-(pi )/(2))]+1 is shown. What is the period of the function? square DONE V

To find the period of the function \(y=\tan \left[\frac{1}{4}\left(x-\frac{\pi}{2}\right)\right]+1\), we need to look at the argument of the tangent function and determine how much needs to change for the function to complete one full cycle.The general form of a tangent function is \(y = \tan(bx - c)\), where the period is given by .In the given function, \(y=\tan \left[\frac{1}{4}\left(x-\frac{\pi}{2}\right)\right]+1\), the coefficient in front of is .Step 1: Identify the coefficient that affects the period of the tangent function.The coefficient is .Step 2: Use the formula for the period of the tangent function.The period of the tangent function is given by .Step 3: Substitute the value of into the formula. Step 4: Calculate the period. Answer: The period of the function \(y=\tan \left[\frac{1}{4}\left(x-\frac{\pi}{2}\right)\right]+1\) is .