Plots of popular functions
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Choose one equation of each type: linear, quadratic, polynomial, rational, exponential, and log. Plot each equation on the same graph. Discuss and compare the appearance of each graph. Describe the plot's shape, the effect of any constants, and behavior for very large or very small x or y.
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In the attached drawing you see the 6 requested plots, each in a separate window to make it easier to see them. Five of the types have two examples drawn, but for the rational I suggest drawing only one example to avoid crowding.
Here is the discussion of the appearance of each type:
LINEAR: y = ax + b
This is a straight line. If a > 0 it is increasing, if a < 0 it is decreasing.
As x tends to infinity, so does y.
QUADRATIC: y = ax^2 + bx + c
It is a parabola with a single extreme: If a > 0 it has a minimum, if a < 0 it has a maximum. The x-coordinate ...
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