2.4.13 Graphing functions using derivatives
Condition: Conduct a complete study of the function and plot the graph: \[ y=\frac{-3 x^{2}+6 x+9}{x^{2}-2 x+13} \]
The study of functions using differential calculus according to a given scheme - finding intervals of monotonicity, convexity, extremum points, vertical, horizontal and oblique asymptotes. Plotting graphs based on the research results.