Question

While a star is being observed through a telescope, the visible light coming from the star shifts from red to blue.

Answer 1

When the light ftom a star is observed at wavelengths shorter than they SHOULD BE, that indicates that the star is moving toward Earth. The wavengths don't shift while you're watching them. They're constant, at a wavelength shorter than they should be. The trick is how to know what the wavelengths of the light you're watching should be.