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有理函数
什么是有理函数？
1. Introduction
Introduction
2. Long-range behavior of rational functions
Long-range behavior of rational functions
3. The domain of a rational function
The domain of a rational function
4. Cost function as a rational function
A drug costs 2500 per gram. What kind of function is the average cost per gram?
5. Rewriting a rational function to find its limit
For r(x) = (3x^2 - 5x + 1)/(7x^2 + 2x - 11), what is the limit as x goes to infinity?
6. Three rational limits by degree comparison
How do the limits at infinity differ when the numerator's degree is equal to, less than, or greater than the denominator's?
7. Domains of rational functions
What is the domain of g(x) = (x^2 - 1)/(x^2 + 3x - 4)?
8. Equal degrees give a finite nonzero limit
If a rational function's numerator and denominator have the same degree, its limit at infinity is the ratio of their leading coefficients.
9. Rational limit at infinity
For r(x) = (3x^2 - 5x + 1)/(7x^2 + 2x - 11), what is the limit as x grows without bound? Enter the exact fraction.