Скачать или смотреть Big Ideas Math [IM3]: 6.2 - Graphing Rational Functions (Lecture & Problem Set)

Graphing rational functions can get very wild. Although the general form y = a/(x - h) + k can often have easily plottable points, sometimes they give unfavorable values and sometimes equations do not appear in this form, though through long/synthetic division you can get there from problems of the form y = (ax + b)/(cx + d).

With y = a/x (much like inverse variation), divide your constant by your x values. No table is needed if you divide by easy values. For example, if I had y = 8/x, I would choose x values of 1, 2, 4, and 8, and their negative counterparts. I wouldn't bother with a 3 or 5 in that case. You'll find vertical and horizontal asymptotes at x = 0 and y = 0, respectively, because we can't ever divide by 0 and we can't get 0 from dividing two nonzero values.

When in the form y = a/(x - h) + k, we now apply translations, and they begin with our asymptotes (VA: x = h, and HA: y = k). Apply the 'a' value as you would previously, only beginning from where both asymptotes intersect.

When graphing out of the form y = (ax + b)/(cx + d), the VA is at x = -d/c (where the denominator can't be zero), and the HA is y = a/c (the division of the linear coefficients since they are equal degree, more explanation in the lecture portion). I prefer to avoid "using tables" still, or rather calculating random points. I can find critical/easy points such as the x-intercept at -b/a (when you set the numerator equal to zero) and the y-intercept at b/d (when you set x equal to zero). From there, you can reflect those points and even possibly determine 'a' without use of any division to get any remaining points you'd like to find.

#47-50 is a block of problems where I attempt to skirt past using the graphing calculator, but they aren't the type of complicated rational functions that I expected, since not all of them had vertical asymptotes and/or x- and y-intercepts. The more features you get off the bat, the better off you are in getting a general understanding of your graph's behavior. I've linked two videos down below for more basic rational functions and more complicated rational functions if you'd like more practice.

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PDF DOWNLOADS

Textbook (6.2): https://smallpdf.com/file#s=d89cff12-...
Graph paper (scaled): https://docdro.id/flV4fYe

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TIMESTAMPS (separated by section)

(0:00:00) Introduction
(0:01:51) Lecture overview
(0:26:13) Problem #1-2
(0:28:10) Problem #3-10
(0:46:34) Problem #11-18
(1:03:14) Problem #19-20
(1:07:24) Problem #21-24
(1:09:05) Problem #25-32
(1:41:50) Problem #33-40
(2:15:37) Problem #41-42
(2:23:57) Problem #43
(2:24:47) Problem #44
(2:26:03) Problem #45
(2:31:14) Problem #46
(2:39:30) Problem #47-50
(2:54:54) Problem #51
(2:55:53) Problem #52
(2:56:45) Problem #53
(2:59:35) Problem #54
(3:01:33) Problem #55
(3:02:52) Problem #56
(3:04:35) Problem #57
(3:07:01) Problem #58

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BIG IDEAS MATH (IM3) PLAYLIST

   • Big Ideas Math [IM3]  

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   • Graphing Rational Functions (practice prob...  
   • Graphing More Complicated Rational Functions