Compton scattering theory question

The question is this: When a photon bounces off an electron, it gives some of its energy to the electron. The photon has no mass, however, and it must continue to travel at speed c. How is its reduced energy manifested?

Now, I do somewhat understand what the Compton effect is and I read in my course notes that in an elastic collision (which is what this is, right?) of a photon with an electron, momentum is conserved. Would it make sense to say that the photon transfers energy to the electron and the frequency decreases because of this loss of energy? Could someone please help clarify? Thanks!

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