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The given fact will relate all of these ideas to the multiplicity of the zero.
Fact
If x = r is a zero of the polynomial P (x) along with multiplicity k then,
1. If the value of k is odd then the x-intercept corresponding to x = r will cross the x-axis
2. If value to k is even then the x-intercept corresponding to x = r will just touch the x-axis and not cross it actually.
Furthermore, if k = 1 then the graph will flatten out at the point x = r .
At last, notice that as we consider x get large in both the +ve or -ve sense (that means at either end of the graph) then the graph will either increase with no bound or decrease without bound. It will always occur with every polynomial and we can employ the following test to find out just what will happen at the endpoints of the graph.
Whereas we are on the subject of function evaluation we have to now talk about piecewise functions. Actually we've already seen an instance of a piecewise function even if we didn'
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