B1. The function $f$ is given by $f(x)=\frac{x^{2}+4 x+3}{x^{2}+1}$. Calculate the zeros, poles, the equation of the asymptote, the coordinates of the intersection points of the graph of the function $f$ with the y-axis, and the intersection points of the graph of the function $f$ with the asymptote. Draw the graph of the function $f$ without calculating the extrema. For which values of the variable $x$ are the values of the function $f$ positive?

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-15.jpg?height=848&width=868&top_left_y=587&top_left_x=640)
B1.

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-24.jpg?height=848&width=857&top_left_y=1226&top_left_x=611)

Calculation of zeros \( x_{1}=-3 \) and \( x_{2}=-1 \) and the conclusion that the function has no poles...

1 point

Writing the equation of the horizontal asymptote \( y=1 \) and the coordinates of the intersection of the graph of the function \( f \) with the y-axis \( x=0 \) and \( y=3 \) or \( N(0,3) \) 1 point Calculation of the coordinates of the intersection of the graph of the function \( f \) with the horizontal asymptote

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-24.jpg?height=65&width=1731&top_left_y=2326&top_left_x=174)

![](https://cdn.mathpix.com/cropped/2024_06_07_7e68135e1a71f8c81168g-24.jpg?height=48&width=1725&top_left_y=2376&top_left_x=177)
Conclusion that the function \( f \) is positive for every \( x \in(-\infty,-3) \cup(-1, \infty) \ldots \ldots \ldots \ldots 1^{*}+1 \) point