How do different factors affect the rate of photosynthesis and transpiration in plants?

Firstly it's important to distinguish that photosynthesis and transpiration are two different processes. Photosynthesis is the process used by plants to convert carbon dioxide and water into gucose and oxygen, using absorbed sunlight. Transpiration is the process whereby water reaching the leaves can be lost by evaporation through the stomata, pulling water up the plant  through the xylem vessels. The rate of photosynthesis can be limited by the factors: temperature, carbon dioxide concentration and light intensity (draw graphs of each factor vs rate of photosynthesis). Temperature increases the rate up to a point and then quickly drops off. This is because the reaction has more kinetic energy up to a certain point, but at around 45 degrees celcius, the enzymes controlling photosynthesis start to be destroyed and cannot function. Light intensity and CO2 concentration increase both cause the rate of photosynthesis to increase while they are the limiting factor, but then plateau once another factor becomes the limiting factor. 

The rate of transpiration can be affected by: light intensity, air movement, temperature and humidity. Increased light intensity will increase the rate of photosynthesis so more water is drawn into the leaves where photosynthesis primarily takes place and therefore the rate of transpiration is greater. Air movement and humidity are linked. On a windy day, increased air movement is likely to remove the water vapour molecules that have just passed out of the plant through the stomata. The air just outside of the stomata is therefore less humid, lowering water vapour concentration and therefore maintaining a concentration gradient for the water to diffuse down. Increased temperature increases the kinetic energy of the water molecules and hence they are removed more quickly.