transformations Flashcards","topicId":"9457a01f-668a-44e8-83b6-28207e62c652","topicSlug":"simple-graph-transformations","cards":[{"id":"571f34af-61be-4792-bdb6-6dfa0dc3327a","cardType":"basic","front":"Which coordinate is changed by a transformation outside $f(x)$?","back":"The $y$-coordinate.","points":1,"mcqOptions":null},{"id":"54b2f5e8-4093-46d7-bbbc-655dec87da69","cardType":"basic","front":"Why do transformations inside $f(x)$ act in the opposite or reciprocal way?","back":"The new $x$-coordinate must compensate for the altered input.","points":2,"mcqOptions":null},{"id":"955c834b-c456-4cfc-b876-65effd7738d4","cardType":"basic","front":"What translation vector transforms $y=f(x)$ into $y=f(x)+a$?","back":"$\\begin{pmatrix}0\\\\a\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"54646944-7e23-47b2-b1b2-7dbfaf0a2aac","cardType":"cloze","front":"The graph of $y=f(x+3)$ is translated [ ].","back":"The graph of $y=f(x+3)$ is translated 3 units left.","points":null,"mcqOptions":null},{"id":"88edc4c1-9764-4197-89f2-fae9e6ca5608","cardType":"basic","front":"Under $y=af(x)$, where does $(p,q)$ move?","back":"$(p,q)\\mapsto(p,aq)$","points":1,"mcqOptions":null},{"id":"1d830051-5583-4e78-85f7-3813c7b0f125","cardType":"cloze","front":"If $|a|>1$, $y=af(x)$ is [ ].","back":"If $|a|>1$, $y=af(x)$ is stretched vertically.","points":null,"mcqOptions":null},{"id":"c018880f-82b9-434a-b09e-b67f5b5431b6","cardType":"cloze","front":"If $0<|a|<1$, $y=af(x)$ is [ ].","back":"If $0<|a|<1$, $y=af(x)$ is compressed vertically.","points":null,"mcqOptions":null},{"id":"58e81caf-eb23-488d-a6d3-e1d270fb83c1","cardType":"basic","front":"What additional transformation occurs in $y=af(x)$ when $a<0$?","back":"A reflection in the $x$-axis.","points":1,"mcqOptions":null},{"id":"266a8660-29a6-4117-a54c-dde9ff0bd45e","cardType":"basic","front":"Why do the roots usually remain unchanged under $y=af(x)$?","back":"Points with $y=0$ remain on the $x$-axis because $a\\times0=0$.","points":2,"mcqOptions":null},{"id":"676e75f9-a03b-4d39-a99c-0987f3ad80ad","cardType":"basic","front":"Under $y=f(x+a)$, where does $(p,q)$ move?","back":"$(p,q)\\mapsto(p-a,q)$","points":1,"mcqOptions":null},{"id":"695e835f-307b-4119-8d3c-b2e1e479f473","cardType":"basic","front":"Under $y=f(ax)$ for $a\\ne0$, where does $(p,q)$ move?","back":"$(p,q)\\mapsto\\left(\\frac{p}{a},q\\right)$","points":1,"mcqOptions":null},{"id":"da8e058d-bab6-4c63-a233-07e0368a5cbf","cardType":"cloze","front":"For $a\\ne0$, $y=f(ax)$ has horizontal scale factor $\\text{[...]}$.","back":"For $a\\ne0$, $y=f(ax)$ has horizontal scale factor $\\boxed{\\frac{1}{|a|}}$.","points":null,"mcqOptions":null},{"id":"039e8ed2-6812-4ce4-8378-c143d3d60cd9","cardType":"cloze","front":"If $|a|>1$, $y=f(ax)$ is [ ].","back":"If $|a|>1$, $y=f(ax)$ is compressed horizontally.","points":null,"mcqOptions":null},{"id":"462a5ef6-b795-4f39-8f84-7e0d5ba55b74","cardType":"basic","front":"What additional transformation occurs in $y=f(ax)$ when $a<0$?","back":"A reflection in the $y$-axis.","points":1,"mcqOptions":null},{"id":"908c1a87-5a42-4c78-9c87-4c472b4df402","cardType":"basic","front":"What graph results from $y=af(x)$ when $a=0$?","back":"The $x$-axis, $y=0$, wherever $f$ is defined.","points":1,"mcqOptions":null},{"id":"946fdffc-a2b6-48e6-bd08-8cc3ff565ec7","cardType":"basic","front":"What graph results from $y=f(ax)$ when $a=0$?","back":"The horizontal line $y=f(0)$, provided $f(0)$ is defined.","points"

1.2.23 Simple graph transformations Flashcards

1.2.23 Simple graph transformations Flashcards