Question about the Sun's Motion My name is Chris, I am a junior and I'm taking an Astronomy class in my high school.
For a homework assignment, I have to explain how the Sun would move across the sky from September 1st through September 30th (assuming that the weather allows viewing)

For example:
In this picture the 

sun is facing west.
If I were to take a picture of this same area at the same time every day for the whole month, 
How would the sun change? Would it go east? 
Would it go lower in the sky? 

I, being a new student to Astronomy, honestly have no clue. 

Thank you and if you need any more info please leave a comment.
Over the year, the sun follows a path known as an annalemma. This is a figure eight shape and is caused by the combination of the Earth's rotation around the Sun and its tilt relative to the plane of the equator.

The analemma can be observed by pointing a camera at the sun, and at the same time each month, take a picture and over lay the images:



Taking a picture every day for a month (in September) would mean that you'd see it lower in the sky, curving slightly as it followed the figure of eight shape of the analemma.

Note:

An analemma can be different on different planets. For example, a Martian analemma is different because its tilt and shape of orbit is different to that of Earth's:




Mercury: Because orbital resonance makes the day exactly two years long, the method of plotting the Sun's position at the same time each day would yield only a single point. However, the equation of time can still be calculated for any time of the year, so an analemma can be graphed with this information. The resulting curve is a nearly straight east-west line.
Venus: There are slightly less than two days per year, so it would take several years to accumulate a complete analemma by the usual method. The resulting curve is an ellipse.
Mars: teardrop
Jupiter: ellipse
Saturn: technically a figure 8, but the northern loop is so small that it more closely resembles a teardrop
Uranus: figure 8 (Uranus is tilted past "sideways" to an angle of 98 degrees. Its orbit is about as elliptical as Jupiter's and more elliptical than Earth's. )
Neptune: figure 8


For more, read this.