Big Ideas Math [IM1]: 3.6 - Transformations of Graphs of Linear Functions (Lecture & Problem Set)

Описание: This may be the right time in the textbook for this section to appear, but this section might not be ready for new learners of graphing, function notation, and transformations for IM1 folks (as we'll do transformations again in a later geometry-based unit). In my longer introduction, I even make a fair assumption that the majority of teachers skip this section entirely. I'll get to point back to this section when we do 4.2 on point-slope form, but even then there is only a loose connection. Beyond this section and reviews, don't expect significantly more transformation talk moving forward until IM2 when we begin transforming nonlinear functions.

There are three distinct types of transformations we will refer to (which applies to nonlinear functions as well): translations, reflections, and stretches/shrinks. Translations are shifts left/right and up/down of your original function, reflections flip the graph over horizontally or vertically, and stretches/shrinks can be either vertical or horizontal by multiplying x's or y's by a factor.

I'll save stating how the equations appear in this description and save it for the long lecture portion, other than to state that horizontal translations and stretches/shrinks appear opposite of what you would do to them in the function. In other words, if something appears as a minus, think of it as a plus, and when multiplying by a number think of its reciprocal. This is because the x values we choose need to counter whatever is affecting our x values. The parameters outside of the function remain unchanged, so positive is positive, etc.

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PDF DOWNLOADS

Textbook (3.6): https://smallpdf.com/file#s=9ae9399f-...
Graph paper (scaled): https://docdro.id/flV4fYe

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TIMESTAMPS (separated by section)

(0:00:00) Introduction
(0:01:09) Lecture overview
(0:34:20) Problem #1-4
(0:40:10) Problem #5-10
(0:46:40) Problem #11-12
(0:49:14) Problem #13-16
(0:52:29) Problem #17-22
(0:57:30) Problem #23-28
(1:00:40) Problem #29-34
(1:03:37) Problem #35-38
(1:05:24) Problem #39-40
(1:10:51) Problem #41-46
(1:23:52) Problem #47-48
(1:29:36) Problem #49-50
(1:34:59) Problem #51
(1:36:54) Problem #52-53
(1:43:16) Problem #54
(1:45:23) Problem #55-60
(2:00:16) Problem #61
(2:02:47) Problem #62
(2:05:55) Problem #63-66
(2:08:33) Problem #67

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