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1. Find the largest domain in the real numbers of the function described by f(x)=5x7.
Solution: The domain is R{7}. You can also describe it in the following ways: "<x<7 or 7<x<" or "(,7)(7,)" or "all real numbers except for 7")

2. Find the domain and range of the function whose graph is given by the following drawing:

Solution: The domain is (0,3] and the range is (2,5].

3. Find the slope of the line containing the points (2,7) and (5,3).
Solution: The slope is slope=m=375(2)=107.

4. What is the slope and the graph of the line y=2x+3?
Solution: The slope is 2. The graph can be seen in the following image:

There are many ways to graph this yourself. For instance from the formula you know that the y-intercept is at (0,3) and from the formula you may deduce that the x-intercept is at (32,0). Then you simply connect the dots.

5. Find the slope and y-intercept of the line described by 2x3y=7.
Solution The easiest way to do this is to rewrite the equation in the form y=mx+b. So solve for y to get y=23x73. Now it is clear that the slope is 23 and the y-intercept is given by the point (0,73).