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==Functions with discontinuities==

==Functions with discontinuities==非连续性函数

Some functions change concavity without having points of inflection. Instead, they can change concavity around vertical asymptotes or discontinuities. For example, the function <math>x\mapsto \frac1x</math> is concave for negative {{mvar|x}} and convex for positive {{mvar|x}}, but it has no points of inflection because 0 is not in the domain of the function.

Some functions change concavity without having points of inflection. Instead, they can change concavity around vertical asymptotes or discontinuities. For example, the function <math>x\mapsto \frac1x</math> is concave for negative {{mvar|x}} and convex for positive {{mvar|x}}, but it has no points of inflection because 0 is not in the domain of the function.

Some functions change concavity without having points of inflection. Instead, they can change concavity around vertical asymptotes or discontinuities. For example, the function <math>x\mapsto \frac1x</math> is concave for negative  and convex for positive , but it has no points of inflection because 0 is not in the domain of the function.

Some functions change concavity without having points of inflection. Instead, they can change concavity around vertical asymptotes or discontinuities. For example, the function <math>x\mapsto \frac1x</math> is concave for negative  and convex for positive , but it has no points of inflection because 0 is not in the domain of the function.

有些函数在没有拐点的情况下改变凹度。相反，它们可以改变垂直渐近线或不连续性周围的凹度。例如，函数 < math > x mapsto frac1x </math > 是凹的表示负的，凸的表示正的，但是它没有拐点，因为0不在函数的域中。

有些函数在没有拐点的情况下也可改变凹度。他们可以通过改变垂直渐近线或非连续性来实现。例如，函数 < math > x mapsto frac1x </math > 在x为负的时候显凹性，在x为正的时候显凸性。但这个函数不具有拐点，因为0不在其定义域内。