Yes, convolutional neural networks are domain-invariant, albeit to some limited extent. We explored the performance impact of domain shift for convolutional neural networks. We did this by designing new synthetic tasks, for which the network’s task was to map images to their mean, median, standard deviation, and variance pixel intensities. We find that the performance drop due to domain shift is related to the shift in pixel values between source and target domain. Colour space transformations seemed to notably impact the network’s performance, opposed to geometric transformations. For the last domain shift we find that the network manages to beat a baseline, from which we can conclude the domain shift is not too severe. Additionally, the findings reveal a less dominant role for feature transferability, for our synthetic regression tasks.