Answer:f the multiplicities of the zeros at x = 3 in the numerator and denominator of the rational function are not equal, it would affect the behavior of the function at x = 3.
When the multiplicities of the zeros are equal, such as both being 1, the function would have a simple crossing at x = 3. The graph of the function would pass through the x-axis at that point.
However, if the multiplicities are not equal, let's say the numerator has a higher multiplicity than the denominator, such as numerator having a multiplicity of 2 and denominator having a multiplicity of 1, the graph would behave differently. In this case, the function would not simply cross the x-axis at x = 3, but rather touch it and turn around. This is known as a "touch and turn" behavior.
The difference in multiplicities affects the number of times the graph interacts with the x-axis at x = 3. If the numerator's multiplicity is higher, it would make the graph "bounce" off the x-axis at that point, causing it to change direction instead of crossing it.
In summary, if the multiplicities of the zeros at x = 3 in the numerator and denominator are not equal, the behavior of the function at x = 3 would change. Instead of a simple crossing, the graph would exhibit a touch and turn behavior, where it touches the x-axis and changes direction.
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