2.7.36 Function properties

Condition: The function is given by different analytical expressions for different areas \( X \) : a) find the discontinuity points of the function, if they exist; b) find one-sided limits and a jump of the function at discontinuity points; c) construct a graph of the function. \( f(x)=\left\{\begin{array}{rc}-3 x, & \text { if } x \leq 0 \\ \tan x, & \text { if } 0 \leq x \leq \frac{\pi}{4} \\ -2, & \text { if } x>\frac{\pi}{4}\end{array}\right. \)