Final answer:
When a star moves towards or away from Earth, its light is shifted to longer or shorter wavelengths, respectively. The red dwarf moving away from Earth and the blue dwarf moving away from Earth would have their light shifted towards longer wavelengths, resulting in a redshift.
Step-by-step explanation:
The Doppler effect is the change in the observed frequency of sound or light waves due to the relative motion between the source of the waves and the observer.
When a star moves towards or away from Earth, its light is shifted to a longer or shorter wavelength, respectively.
In this case, the red dwarf moving away from Earth at 39.1 km/s would have its light shifted towards longer wavelengths, resulting in a redshift.
Similarly, the blue dwarf moving away from Earth at 25.9 km/s would also experience a redshift.
On the other hand, the red giant moving towards Earth at 23.3 km/s would have its light shifted towards shorter wavelengths, resulting in a blueshift.
The yellow dwarf moving transversely at 15.1 km/s would not exhibit any shift in its light because its motion is perpendicular to the line of sight.
The red dwarf moving transversely at 14.1 km/s would also not show any shift in its light.