Calling those who understand wave mechanics?

So, I have a question I can't wrap my head around nor ask a database if it's been asked before.

Photons are the basic particles of light, and light is basically the electromagnetic spectrum, which ranges in frequency and wavelength.

I wanted to know what happens when frequency hits 0, which causes wavelength to become infinite? It is graphed as a line, but what is it called then, does it no longer become a wave? And what happens when frequency hits infinity and wavelength becomes 0? I'm basing this off of the wave model. Or is the wave model only limited to frequencies(f) 0<f>∞ and wavelengths(w) 0<w>∞?

Y=-2x+1

Light = fried potatoe