1. Graphing Polynomial Functions
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As we can see from the graphs of Exploration 1, the graphs for cubic polynomial functions have different behaviors when x approaches positive infinity as opposed to what it has as x approaches negative infinity. Note that the function increases in one direction and decreases in the other one.
On the other hand, the graphs of a quartic polynomial function have the same behavior when x approaches positive infinity as that it has when x approaches negative infinity. These can be seen in the graphs below. Note that the function either increases or decreases indefinitely in both directions.
