Draw the graph of `y = tan^(-1)(tan x)`

Explanation

To draw the graph of \( y = \tan^{-1}(\tan x) \), we need to understand the behavior of the function and its range. Here’s a step-by-step solution:

### Step 1: Understand the Function
The function \( y = \tan^{-1}(\tan x) \) is defined for all \( x \) where \( \tan x \) is defined. The function \( \tan x \) has a period of \( \pi \), meaning it repeats every \( \pi \) units.

### Step 2: Determine the Range of \( y \)
The range of \( y = \tan^{-1}(x) \) is \( \left(-\frac{\pi}{2}, \frac{\pi}{2}\right) \). However, since \( \tan x \) is periodic, we need to analyze how \( y \) behaves over intervals of \( \pi \).

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