In the realm of mathematics, identifying zeros within a function entails determining the x-values at which the function equates to zero. The term 'multiplicity of a zero' denotes the frequency of occurrence of that particular zero as a root. Importantly, the multiplicity of a zero influences the behavior of the graph at the zero. Specifically, even multiplicities result in a bounce, while odd multiplicities cause the graph to pass through.
Topic | Problem | Solution |
---|---|---|
None | Given the function \(f(x) = (x + 1)(x - 2)^2(x + … | Firstly, set \(f(x)\) to zero and solve for \(x\): \[0 = (x + 1)(x - 2)^2(x + 3)^3\] |