Your task is just get a polyhedron representing the view area, and check if your objects bounding boxes are inside it.
The blue are the near and far plane, the red and blue, together are a convex POLYHEDRON. Some engines give you helping methods to get this polyhedron. It's usually a pyramid(from camera to far plane), a trapezium(from near plane to far plane) or simply, a box for a orthographic projection. There are a lot of formulas about how to calculate if one box is inside a convex polyhedron on the web, This link is an awesome example.
I thought a little more, and other way, maybe cheaper to try this, is to calculate the angle between the object and the camera, see if it's withing fovy angle, farther than near plane, and nearer than far plane. Depending on how you do it, this could be cheaper but i'm not sure. Trig functions usually gets a great CPU time.
Some links to help you:
http://www.flipcode.com/archives/Frustum_Culling.shtml - Frustum culling is the technique that makes you don't draw what's outside the camera range. This link has how you can build a frustum bounding sphere, that may be very useful to you.
http://www.yaldex.com/game-programming/0131020099_ch22lev1sec1.html - Point inclusion, AABB tests and Point-in-Convex Polygon. To check if the object is inside the camera range.