nd functions (A-level only) Flashcards","topicId":"b573749e-6501-4616-9935-e6d921ee7262","topicSlug":"algebra-and-functions-23","cards":[{"id":"2519df0f-694e-4d29-8637-6a9470984266","cardType":"basic","front":"Which coordinate is changed by a transformation outside $f(x)$?","back":"The $y$-coordinate.","points":1,"mcqOptions":null},{"id":"dca331cb-7fee-4f5e-b2fe-808dbd8434a6","cardType":"basic","front":"Which coordinate is changed by a transformation inside $f(x)$?","back":"The $x$-coordinate.","points":1,"mcqOptions":null},{"id":"c67b9ee3-09f3-4bdb-9e47-f48d9b332990","cardType":"basic","front":"How does $y=af(x)$ map a point $(x,y)$?","back":"$(x,y)\\mapsto(x,ay)$","points":1,"mcqOptions":null},{"id":"671b422c-062d-4964-95f9-3408cfe852f6","cardType":"basic","front":"What happens to $y=f(x)$ when $a=0$ in $y=af(x)$?","back":"The graph becomes $y=0$.","points":1,"mcqOptions":null},{"id":"91989838-b885-43b8-b452-0d7f4baa5dcc","cardType":"basic","front":"Which reflection occurs in $y=af(x)$ when $a<0$?","back":"Reflection in the $x$-axis.","points":1,"mcqOptions":null},{"id":"ea7e314c-8c24-4e14-a09a-b28bc1d00cd3","cardType":"cloze","front":"In $y=af(x)$, $a>1$ produces a [ ], while $01$ produces a vertical stretch, while $01$ produces a vertical stretch, while $0[ ].","back":"In $y=af(x)$, $a>1$ produces a vertical stretch, while $0vertical compression.","points":null,"mcqOptions":null},{"id":"f394a2a5-66e9-4eb1-9d5d-5d1e56a69c45","cardType":"basic","front":"Why are points on the $x$-axis invariant under $y=af(x)$?","back":"Their $y$-coordinate is zero, so multiplying it changes nothing.","points":2,"mcqOptions":null},{"id":"b00b515a-690b-4485-b7e2-14a8de06161d","cardType":"basic","front":"How does $y=f(x)+a$ map a point $(x,y)$?","back":"$(x,y)\\mapsto(x,y+a)$","points":1,"mcqOptions":null},{"id":"30ac7304-b5e5-449f-ba81-008e33645332","cardType":"basic","front":"What is the translation vector for $y=f(x)+a$?","back":"$\\begin{pmatrix}0\\\\a\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"32d1b14b-8095-489f-a247-81d94f82e1e1","cardType":"basic","front":"Where does the turning point $(0,0)$ move under $y=x^2-5$?","back":"$(0,-5)$","points":1,"mcqOptions":null},{"id":"fdbf246b-a4de-41c4-8bfe-1c8921a76691","cardType":"basic","front":"How does $y=f(x+a)$ map a point $(x,y)$?","back":"$(x,y)\\mapsto(x-a,y)$","points":1,"mcqOptions":null},{"id":"6fcc6321-1bc4-48fa-bb55-55e7022b3440","cardType":"cloze","front":"The graph of $y=f(x+a)$ has translation vector $\\text{[...]}$, so $f(x+3)$ moves left by 3 units.","back":"The graph of $y=f(x+a)$ has translation vector $\\boxed{\\begin{pmatrix}-a\\\\0\\end{pmatrix}}$, so $f(x+3)$ moves left by 3 units.","points":null,"mcqOptions":null},{"id":"d8dceab7-78ef-40b0-b2b5-53e2091d7892","cardType":"cloze","front":"The graph of $y=f(x+a)$ has translation vector $\\begin{pmatrix}-a\\\\0\\end{pmatrix}$, so $f(x+3)$ moves [ ].","back":"The graph of $y=f(x+a)$ has translation vector $\\begin{pmatrix}-a\\\\0\\end{pmatrix}$, so $f(x+3)$ moves left by 3 units.","points":null,"mcqOptions":null},{"id":"9d77b4be-da09-449d-b571-59abffa6c427","cardType":"basic","front":"Where does a maximum at $(4,7)$ move under $y=f(x-6)$?","back":"$(10,7)$","points":1,"mcqOptions":null},{"id":"0be2a260-3a55-43a6-b885-cd37def2b2b9","cardType":"basic","f

3.1.7 Algebra and functions (A-level only) Flashcards

3.1.7 Algebra and functions (A-level only) Flashcards