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urp:algebra [2021-12-19] nerf_herder [Functions] |
urp:algebra [2021-12-19] nerf_herder [Functions] |
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* horizontal asymptotes (HA) is when x goes to infinity, look at highest order of x in numerator and denominator: | * horizontal asymptotes (HA) is when x goes to infinity, look at highest order of x in numerator and denominator: | ||
* y = axⁿ / bxᵏ | * y = axⁿ / bxᵏ | ||
- | * if n > k : no HA | ||
* if n < k : HA = 0 | * if n < k : HA = 0 | ||
* if n = k : HA = a/b | * if n = k : HA = a/b | ||
- | * oblique (diagonal) - approaches the line y = mx+b | + | * if n > k : no HA |
- | * look halfway down the page here: https://www.mathsisfun.com/algebra/rational-expression.html | + | * if n = k+1 : oblique (diagonal) asymptote - approaches the line y = mx+b (from polynomial long division) |
- | * if power of x in numerator > power of x in denominator: asymptote = 0 | + | * if n > k+1 : no asymptote |
- | * if power of x in numerator = power of x in denominator: asymptote = horizontal, not zero (ratio of largest coefficients) | + | |
- | * if power of x in numerator = 1 less than power of x in denominator: asymptote = oblique (definition of line, from polynomial long division) | + | look halfway down the page here: https://www.mathsisfun.com/algebra/rational-expression.html |
- | * if power of x in numerator > 1 less than power of x in denominator: asymptote = none | + | |
====Interest, half life, amortization==== | ====Interest, half life, amortization==== |