Differences between low-pass, band-pass, notch filters
First,note that your drawn filter responses are one dimensional filters. 

Notch filter, selectively suppresses some frequency bands that are not of interest. One of the well known applications of notch filter in image processing is image denoising. As an example, consider the following image, which is corrupted by periodic noise (the tiled parallel bars).

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If we take Fourier transform of the image, it will be something like this:


Based on our prior observations and knowledge we know this image should not have larges peaks other that central section, so those other peaks are the noise and are responsible for the parallel bars in the image. To remove those, we can apply a notch filter which allows all frequencies to pass, except for frequency components of the periodic noise.


  a notch filter is composed of the product of two high-pass filters


I would say it is product of a low-pass and a high-pass filter.