understanding Multiplicity
in my books of algebra it talks about polynomial functions and their zeros
Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the x-axis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the x-axis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
what does flatten out means ?
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$\begingroup$What the book is probably trying to convey is that when a polynomial has a repeated root, the slope of the function tends to approach zero when $y=0$. Take, for example, the graph of $y=\left(x+1\right)^3\left(x+3\right)$:
The graph has a repeated root of $x=-1$ with a multipicity of 3. The slope of the graph approaches zero as $x$ approaches -1.
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