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Unformatted text preview: epts of the graph. Also, recall that
x-intercepts can either cross the x-axis or they can just touch the x-axis without actually crossing
Notice as well from the graphs above that the x-intercepts can either flatten out as they cross the
x-axis or they can go through the x-axis at an angle.
The following fact will relate all of these ideas to the multiplicity of the zero.
If x = r is a zero of the polynomial P ( x ) with multiplicity k then,
1. If k is odd then the x-intercept corresponding to x = r will cross the x-axis.
2. If k is even then the x-intercept corresponding to x = r will only touch the x-axis and not
actually cross it.
Furthermore, if k > 1 then the graph will flatten out at x = r .
Finally, notice that as we let x get large in both the positive or negative sense (i.e. at either end of
the graph) then the graph will either increase without bound or decrease without bound. This will
always happen with every polynomial and we can use the following test to determine just what
will happen at the endpoints of the graph.
Leading Coefficient Test
Suppose that P...
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This note was uploaded on 06/06/2012 for the course ICT 4 taught by Professor Mrvinh during the Spring '12 term at Hanoi University of Technology.
- Spring '12