Question

# Given?(?,?)= 9− ?^2 a). State the function’s domain and range. b). Sketch the surface in 3-D....

Given?(?,?)= 9− ?^2
a). State the function’s domain and range.

b). Sketch the surface in 3-D. Be sure to clearly label your axes and label any points on the surface that cross an axis.

c). On a separate graph from part (b), sketch the following level curves in the domain of the function: f(x, y) = 0, f(x, y) = 5, and f(x, y) = 9. Label the value of f(x, y) on each level curve.

a) The function has the domain of all real values for the inpput x, and the range is 0 ≤ z ≤ 9

b) The curve is a parabolic cylinder, that is inerted along Z axis when seen from XY plane. A graphing calculator can show below sketch.

It cuts the X axis at ±3 and crosses the Z axis at z = 9

c) All level curves are straight lines on the XY plane , perpendicular to th X axis.

f(x, y) = 0 is the set of lines x = ±3, z = 0

f(x, y) = 5 is the set of lines x = ±2, z = 5

f(x, y) = 9 is the line x = 0, z = 9