Example 3.21. Find the points of discontinuity of the function

$$
z=\frac{x y+1}{x^{2}-y}
$$
Solution. The function will lose its meaning if the denominator becomes zero. But $x^{2}-y=0$ or $y=x^{2}$ is the equation of a parabola. Therefore, the given function has a line of discontinuity, which is the parabola $y=x^{2}$.