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有理函数的关键特征(续)
说一个有理函数在某点有一个「洞」,这是什么意思,又是什么样的代数结构导致了这种行为?
1. Summary
Summary
2. Zero, asymptote and hole together
For r(x) = (x^2 - 16)/(x + 4), what does the graph look like at x = -4?
3. Removable discontinuity value
A rational function r(x) = k/(x - a) + b has a horizontal asymptote y = -3/7, a vertical asymptote at x = 5/2, and r(0) = 4. What is k? Give the exact fraction.
4. Inverting a rational function
Why does r(x) = -3/(x - 4) + 5 have an inverse, and what is it?
5. Average rate of change as a rational function
For f(x) = x^2, why is A(x) = (f(x) - f(1))/(x - 1) a rational function, and what is its limit at x = 1?
6. A rational function can be inverted when it is one-to-one
A rational function with a horizontal asymptote can still have an inverse function.