Describe and show how the Earth's temperature structure would change in each of the following two cases. Describe how the temperature graph would appear different, and why these changes would occur. Include a sketch of the revised temperature graph in each case. a) If the Sun was producing no X-rays? b) If the Sun was producing more ultraviolet light?

Earth's temperature would not change considerably in either scenario, as these rays produced by the sun do not reach the Earth's surface due to the planet's thick atmosphere.  The sun's corona creates the x-rays that the star produces.  Due to their short wavelengths, they cannot penetrate Earth's atmosphere; this is fortunate because x-ray radiation is a known carcinogen.  
A great deal of UV light is blocked by Earth's ozone layer.  UV light is responsible for sunburns, and it is also considered a factor in the formation of skin cancers.  Scientists do not worry so much that the sun will produce more UV light but that the Earth will take on more of it due to a depleting ozone layer.  An increase in UV light from the sun would not affect Earth's temperature a great deal; however, the thing that would affect your temperature graph would be the trapping of heat energy from the sun due to greenhouse gases.