Consider the following function.
\(f(x, y) = \frac{-5x}{x^2 + y^2 + 1}\)
(a) Find the domain and range of the function.
Domain:
\(\{(x, y): x \ge 0, y \ge 0\}\)
\(\{(x, y): y \ge 0\}\)
\(\{(x, y): x \ge 0\}\)
\(\{(x, y): x \ne 0, y \ne 0\}\)
\(\{(x, y): x\text{ is any real number, }y\text{ is any real number}\}\)
Range: (Enter your answer using interval notation.)
(b) Identify the points in the xy-plane at which the function value is 0.
All points in the xy-plane.
All points on the x-axis.
The function value is never 0.
All points on the y-axis.
All points where \(x = y\).
(c) Does the surface pass through all the octants of the rectangular coordinate system? Give reasons for your answer.
When x is positive, z is When x is negative, z is So, the surface pass through all octants.
