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1. Find the largest domain in the real numbers of the function described by f(x)=5x−7.
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=−3−75−(−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 2x−3y=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=23x−73. Now it is clear that the slope is 23 and the y-intercept is given by the point (0,−73).