From e43e654c21af54900b48aad2201f0b1115e08b93 Mon Sep 17 00:00:00 2001 From: Joshua Potter Date: Fri, 6 Dec 2024 15:03:24 -0700 Subject: [PATCH] Add missing scaling flashcards. --- .../plugins/obsidian-to-anki-plugin/data.json | 4 +- notes/_journal/2024-12-06.md | 2 +- notes/geometry/cartesian.md | 156 +++++++++++++++++- 3 files changed, 156 insertions(+), 6 deletions(-) diff --git a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json index 8f35c65..360d66e 100644 --- a/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json +++ b/notes/.obsidian/plugins/obsidian-to-anki-plugin/data.json @@ -945,7 +945,7 @@ "_journal/2024-11/2024-11-08.md": "806bbade5f8339579287687f9433334e", "_journal/2024-11/2024-11-07.md": "434ec3f15d7065ea740127aa8477dd17", "x86-64/directives.md": "019c1c1d04efb26c3e8758aac4543cc7", - "geometry/cartesian.md": "662f241b94c78dfb8ac1e7fd0c1120e8", + "geometry/cartesian.md": "67d6920732d1ab7dd72e12fba28cf8bc", "geometry/index.md": "cac68c1b624dbb0552e56cce47bcc21d", "_journal/2024-11-10.md": "5478337fd2017b99d0b359713a511e66", "_journal/2024-11/2024-11-09.md": "46f3a640223ef533f4523837b67b57c3", @@ -996,7 +996,7 @@ "_journal/2024-12/2024-12-03.md": "54480a38f1e16e48529cbb99c5349c74", "_journal/2024-12-05.md": "efc79d779a0b0354fc0e8658b074a693", "_journal/2024-12/2024-12-04.md": "965f6619edf1002d960203e3e12a413b", - "_journal/2024-12-06.md": "8ab4dc393cc7d68012b47e28029fd16d", + "_journal/2024-12-06.md": "d75323d0fec57f4fc1f13cb4370df18d", "_journal/2024-12/2024-12-05.md": "4f3b1e7a43e01cc97b0eed6fbc6c1f96", "calculus/integrals.md": "a7ef5031ca474cd9d37c1aea85e96237" }, diff --git a/notes/_journal/2024-12-06.md b/notes/_journal/2024-12-06.md index d49beaf..bf8fb18 100644 --- a/notes/_journal/2024-12-06.md +++ b/notes/_journal/2024-12-06.md @@ -9,4 +9,4 @@ title: "2024-12-06" - [ ] Korean (Read 1 Story) * Begin notes on [[integrals]], starting with those of step functions. -* Notes on [[cartesian#Shifting|shifting]] graphs. \ No newline at end of file +* Notes on [[cartesian#Shifting|shifting]] and [[cartesian#Scaling|scaling]] graphs. \ No newline at end of file diff --git a/notes/geometry/cartesian.md b/notes/geometry/cartesian.md index 049b260..608ce83 100644 --- a/notes/geometry/cartesian.md +++ b/notes/geometry/cartesian.md @@ -151,9 +151,23 @@ Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” acces END%% +%%ANKI +Cloze +{1:Adding} is to {2:shifting} as {2:multiplying} is to {1:scaling}. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +{1:Dividing} is to {2:scaling} as {2:subtracting} is to {1:shifting}. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + ### Shifting -A **vertical shift** adds a constant to every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A **horizontal shift** adds a constant to every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged. +A **vertical shift** adds/subtracts a constant to every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A **horizontal shift** adds/subtracts a constant to every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged. %%ANKI Basic @@ -165,18 +179,40 @@ END%% %%ANKI Basic -A {vertical} shift adds a constant to the {$y$}-coordinates of a graph. +Which of the two fundamental graph translations is considered "rigid"? +Back: Shifts. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Basic +A {vertical} shift adds/subtracts a constant to the {$y$}-coordinates of a graph. Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). END%% %%ANKI Cloze -A {horizontal} shift adds a constant to the {$x$}-coordinates of a graph. +A {horizontal} shift adds/subtracts a constant to the {$x$}-coordinates of a graph. Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). END%% +%%ANKI +Cloze +A {horizontal} shift corresponds to adding/subtracting the {input} of a function. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +A {vertical} shift corresponds to adding/subtracting the {output} of a function. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + %%ANKI Basic Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $f(x + k)$? @@ -275,6 +311,120 @@ Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” acces END%% +### Scaling + +A **vertical scaling** will multiply/divide every $y$-coordinate of a graph, leaving the $x$-coordinate unchanged. A **horizontal scaling** will multiply/divide every $x$-coordinate of a graph, leaving the $y$-coordinate unchanged. + +Scaling is also known as **stretching** and **compressing**. + +%%ANKI +Basic +What does it mean for a scaling of a graph to be non-rigid? +Back: A scaling changes the size and/or shape of the graph. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Basic +A {vertical} scaling multiplies/divides the {$y$}-coordinates of a graph. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +A {horizontal} scaling multiplies/divides the {$x$}-coordinates of a graph. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Basic +Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $kf(x)$? +Back: A vertical scaling. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Basic +Let $f(x)$ be a function and $k$ be a constant. What kind of translation is $f(kx)$? +Back: A horizontal scaling. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +A {vertical} scaling corresponds to multiplying/dividing the {output} of a function. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +A {horizontal} scaling corresponds to multiplying/dividing the {input} of a function. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(x)$ be a function and $k$ be a constant. $f(kx)$ is horizontally {stretched} when {$0 < \lvert k \rvert < 1$}. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(x)$ be a function and $k$ be a constant. $kf(x)$ is vertically {stretched} when {$\lvert k \rvert > 1$}. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(x)$ be a function and $k$ be a constant. $kf(x)$ is vertically {compressed} when {$0 < \lvert k \rvert < 1$}. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(x)$ be a function and $k$ be a constant. $f(kx)$ is horizontally {compressed} when {$\lvert k \rvert > 1$}. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(t)$ be a function of time. Vertically compressing $f(t)$ means it takes {more} time to reach a value. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(t)$ be a function of time. Horizontally compressing $f(t)$ means it takes {less} time to reach a value. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(t)$ be a function of time. Vertically stretching $f(t)$ means it takes {less} time to reach a value. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + +%%ANKI +Cloze +Let $f(t)$ be a function of time. Horizontally stretching $f(t)$ means it takes {more} time to reach a value. +Reference: James Jones, “Shifting, Reflecting, and Stretching Graphs,” accessed December 6, 2024, [https://people.richland.edu/james/lecture/m116/functions/translations.html](https://people.richland.edu/james/lecture/m116/functions/translations.html). + +END%% + ## Bibliography * “Cartesian Coordinate System,” in _Wikipedia_, October 21, 2024, [https://en.wikipedia.org/w/index.php?title=Cartesian_coordinate_system](https://en.wikipedia.org/w/index.php?title=Cartesian_coordinate_system&oldid=1252434514).