Single transformations of graphs Flashcards","topicId":"f2e9363c-ff36-47e8-b24d-00e2bacdf30e","topicSlug":"single-transformations-of-graphs","cards":[{"id":"87fbb5d3-ea8b-47cd-b190-4cf2f09709c5","cardType":"basic","front":"Does a change outside $f$ act vertically or horizontally?","back":"It acts vertically by changing output values.","points":1,"mcqOptions":null},{"id":"cdc088fd-b800-4772-8a1b-28ae90c7f6ca","cardType":"basic","front":"Does a change inside $f$ act vertically or horizontally?","back":"It acts horizontally by changing input values.","points":1,"mcqOptions":null},{"id":"c3f2884b-5a12-47da-8196-d0ddb75882c5","cardType":"cloze","front":"Under $y=af(x)$, a point maps as $\\text{[...]}$.","back":"Under $y=af(x)$, a point maps as $\\boxed{(x,y)\\mapsto(x,ay)}$.","points":null,"mcqOptions":null},{"id":"377b4bde-433f-4e5b-9a2f-0cf26d60f582","cardType":"basic","front":"What transformation does $y=af(x)$ produce when $a>0$?","back":"A stretch parallel to the $y$-axis with scale factor $a$.","points":1,"mcqOptions":null},{"id":"b0c20f38-bebd-45b1-81a8-1c76526262bf","cardType":"basic","front":"Describe fully the transformation from $y=f(x)$ to $y=-\\frac12f(x)$.","back":"

Reflection in the $x$-axis
Vertical scale factor $\\frac12$

","points":3,"mcqOptions":null},{"id":"44b6399d-ecee-47e1-beed-19bfe1c142e3","cardType":"basic","front":"Which points are invariant under $y=af(x)$?","back":"Points on the $x$-axis.","points":1,"mcqOptions":null},{"id":"8ef0b550-185b-4090-99a9-7d3ee73961ba","cardType":"cloze","front":"The graph of $y=f(x)+a$ has translation vector $\\text{[...]}$.","back":"The graph of $y=f(x)+a$ has translation vector $\\boxed{\\begin{pmatrix}0\\\\a\\end{pmatrix}}$.","points":null,"mcqOptions":null},{"id":"02020872-0175-4f62-b468-fbb76f41407b","cardType":"basic","front":"What happens to the horizontal asymptote $y=c$ under $y=f(x)+a$?","back":"It becomes $y=c+a$.","points":1,"mcqOptions":null},{"id":"ca945d7c-d581-4fdd-ba27-1b110ef3cb67","cardType":"basic","front":"The graph $y=x^2$ is translated down 5 units. What is its new equation?","back":"$y=x^2-5$","points":1,"mcqOptions":null},{"id":"186cd1df-31d3-4419-9bc2-fbd81ac3fa02","cardType":"cloze","front":"Under $y=f(x+a)$, a point maps as $\\text{[...]}$.","back":"Under $y=f(x+a)$, a point maps as $\\boxed{(x,y)\\mapsto(x-a,y)}$.","points":null,"mcqOptions":null},{"id":"3bf312ee-8792-414b-a51b-1886331c4d73","cardType":"basic","front":"In which direction does $y=f(x+3)$ translate the graph of $y=f(x)$?","back":"3 units left.","points":1,"mcqOptions":null},{"id":"7212e73a-301c-497a-9385-8930c72183a6","cardType":"basic","front":"How is a translation $k$ units right written as a transformed function?","back":"$y=f(x-k)$","points":1,"mcqOptions":null},{"id":"47b1e639-24fb-438d-a4e8-7e1b2c202df5","cardType":"basic","front":"Why do horizontal translations move opposite to the sign inside $f$?","back":"The new input must compensate for the added value to produce the original output.","points":2,"mcqOptions":null},{"id":"38eb2336-4737-4873-819d-10af3c74fa7d","cardType":"basic","front":"The graph $y=\\frac1x$ moves 4 units right. State its new equation.","back":"$y=\\frac{1}{x-4}$","points":1,"mcqOptions":null},{"id":"7f3ba7f8-977a-4bfb-86a4-14632fc19338","cardType":"basic","front":"After translating $y=\\frac1x$ four units right, what is its vertical asymptote?","back":"$x=4$","points":1,"mcqOptions":null},{"id":"524d3830-3df6-46cd-8fe4-5f2c216e7c57","cardType":"cloze","front":"For $a\\ne0$, under $y=f(ax)$ a point maps as $\\text{[...]}$.","back":"For $a\\ne0$, under $y=f(ax)$ a point maps as $\\boxed{\\left(x,y\\right)\\mapsto\\left(\\frac{x}{a},y\\right)}$.","points":null,"mcqOptions":null},{"id":"c9e9b88d-9530-4b0e-98a2-de25aa39282f","cardType":"basic","front":"What is the horizontal scale factor for $y

1.4.7 Single transformations of graphs Flashcards

1.4.7 Single transformations of graphs Flashcards