Domain: -3 to 3, because 9-x²≥0 so x²≤9, |x|≤3.
Range: -4.5 to 4.5, because d(x√(9-x²))/dx=-x²/√(9-x²)+√(9-x²)=0 (max/min) when -x²+9-x²=0=9-2x².
x=±√(9/2)=±3/√2=±3√2/2, and y=±(3√2/2)√(9-9/2)=±9/2=±4.5.
Intercepts: y=0 when x=±3 so x intercepts are at -3 and 3. When x=0 y=0, so y intercept is at 0.
No asymptotes but graph only exists between and at the x intercepts.
Minimum (concave up) at (-3√2/2, -4.5) and maximum (concave down) at (3√2/2, 4.5).
Graph to follow (internal system error prevents upload—ads interfere with upload)...
Description of graph: starts at (-3,0), dips to minimum at (-3√2/2,-4.5), rises to pass through (0,0) then continues to rise to maximum at (3√2/2,4.5) and then falls to its termination at (3,0). The left and right halves of the graph are symmetrical but inverted—y is an odd function: y(x)=-y(-x).