Would the Doppeler effect be incorrect to use as evidence to support an expanding universe? In our science class we have a question to answer, which is 'explain how redshift supports the idea of an expanding universe'. 
I am not sure how to answer this question, as I know that there are 'different types' of redshifts. The one we (my class) were focusing on for this topic was the Doppeler effect. We were told that the galaxies were moving away from us, so that causes the light to shift. I have explained it like this in the past and have gotten it correct, however, I also know that on a scale so large, that space itself expansing is causing the redshift. So I am not sure how I should answer this question because I feel like the teacher is asking us to explain the doppeler effect, not cosmological redshift. So if I explain it using the Doppeler effect example, would the answer generally be incorrect because it is cosmological redshift that supports an expanding universe?
 A: Cosmological and Doppler redshifts are equivalent. 
We usually use the "Cosmic expansion stretches light wavelengths" explanation, because it is intuitive, and a completely valid explanation.
However, we could equally well see cosmological redshift as the accumulated Doppler redshifts between the local rest frames of every set of neighboring points in the Universe.
As a photon travels through expanding space, it travels through a series of spatial points, which each has their own frame of being "at rest", slightly different from that of the neighboring points. As the photon travels, this difference builds up, and redshift accumulates. 
If I am at point A, and a photon is emitted at point B some cosmological distance from me, an observer at rest at an intermediate point C will see the light from point B as less redshifted than I do at point A. But from my point of view, I might as well say -- and equally true -- that tpoint C is also moving relative to me, and that the difference in perceived redshifts is due to their velocity, not because anybody is stretching their light waves.  
Of course, the danger of using the simple Doppler Shift framework of explanation is that it may lead to wrong conclusions like e.g. the widespread misconception that the redshift approaces infinity as the recession velocity approaches $c$, that either galaxies can never recede form us faster than light (they can) or that we can never see galaxies receding faster than light (we can). These are usually based on misunderstandings about how Relaytivity works (which is not so strange, it can be quite difficult to understand and I certainly drew all these wrong conclusions myself until I was taught that they were wrong). 
