You will need to show that it makes a cell grow or divide, under conditions where it wouldn't otherwise do it. For example, in serum free media, a fibroblast will just sit there and not do anything. Then you add fibroblast growth factor, and it starts dividing.
I commend eBiosciences for publishing a compilation of all the commonly used growth factor assays with detailed protocols http://www.ebioscience.com/knowledge-center/functional-activity/cytokine-bioassays.htm.
When you show that protein X is one of the growth factors, you have to find the receptor localized at the cellular membrane. After you find out what kind of cells are sensitive to proteinX in terms of proliferation, NP-40-treated cell lysates enriched in cellular membrane proteins should be analyzed in the IP and LC/MS experiments to reveal which molecule binds to the protein X as its ligand.
Measurement of the activity of the mitogen-activated protein kinase (MAP kinase) following the stimulation by your protein on various cells after starving might be another option as most growth factors can activate this signalling pathway if the there are receptors for your protein on these cells.