Type":"basic","front":"Evaluate $|3-8|+|-4|$.","back":"$9$","points":1,"mcqOptions":null},{"id":"40868d69-2516-47b5-ad83-aeb6c3510c38","cardType":"basic","front":"Why can $|x|$ never be negative?","back":"It represents a distance from zero.","points":2,"mcqOptions":null},{"id":"a4847108-b846-4d31-a567-a2bc43a80cb2","cardType":"cloze","front":"For $x\\ge 0$, $|x|=$ $\\text{[...]}$.","back":"For $x\\ge 0$, $|x|=$ $\\boxed{x}$.","points":null,"mcqOptions":null},{"id":"0f8b8e25-623f-480c-8767-048c5ee6942b","cardType":"cloze","front":"For $x<0$, $|x|=$ $\\text{[...]}$.","back":"For $x<0$, $|x|=$ $\\boxed{-x}$.","points":null,"mcqOptions":null},{"id":"758df118-bc84-48de-a636-093cf0a12bbe","cardType":"basic","front":"What distance does $|x-a|$ represent?","back":"The distance between $x$ and $a$.","points":1,"mcqOptions":null},{"id":"3db58063-924f-4f3f-814e-b378ee35d6ae","cardType":"cloze","front":"The range of $y=|x|$ is $\\text{[...]}$.","back":"The range of $y=|x|$ is $\\boxed{y\\ge 0}$.","points":null,"mcqOptions":null},{"id":"fbc00251-afa9-4103-b77f-e110559d4538","cardType":"cloze","front":"Because $|-x|=|x|$, the graph of $y=|x|$ is symmetric about the [ ].","back":"Because $|-x|=|x|$, the graph of $y=|x|$ is symmetric about the $y$-axis.","points":null,"mcqOptions":null},{"id":"6abbe067-1cb3-4b79-9a0a-fdcf15441055","cardType":"basic","front":"Where is the vertex of $y=a|x-h|+k$?","back":"$(h,k)$","points":1,"mcqOptions":null},{"id":"b976bbd4-09c0-49b3-bc7b-dddce6bf55af","cardType":"basic","front":"How does $a<0$ affect the graph of $y=a|x-h|+k$?","back":"It reflects in the $x$-axis, so it opens downwards.","points":2,"mcqOptions":null},{"id":"75022789-88fa-4c1d-81a1-400558d9542d","cardType":"basic","front":"Where is the vertex of $y=|x-3|$?","back":"$(3,0)$","points":1,"mcqOptions":null},{"id":"8d5e8cae-c8b0-4bf6-8b9b-9a5fba698021","cardType":"basic","front":"How is $y=|f(x)|$ constructed from $y=f(x)$?","back":"Reflect sections below the $x$-axis in the $x$-axis.","points":2,"mcqOptions":null},{"id":"5a9b7c87-9f0c-46ac-8931-d489ee9f0441","cardType":"basic","front":"How is $y=f(|x|)$ constructed from $y=f(x)$?","back":"

Keep the section for $x\\ge 0$.
Reflect it in the $y$-axis.
Discard the original section for $x<0$.

","points":3,"mcqOptions":null},{"id":"e30e7770-443e-4401-ad74-136a0f773a50","cardType":"basic","front":"For $k>0$, what cases must be solved when $|A|=k$?","back":"$A=k$ or $A=-k$","points":2,"mcqOptions":null},{"id":"892a0565-cea7-411a-9645-4d13406906f4","cardType":"basic","front":"What if $|A|=k$ and $k<0$?","back":"There are no real solutions because $|A|\\ge 0$.","points":2,"mcqOptions":null},{"id":"047c3457-e479-45ac-9d7c-e1a65dc9b40b","cardType":"basic","front":"Solve $|2x-5|=7$.","back":"$x=6$ or $x=-1$","points":2,"mcqOptions":null},{"id":"bc3beb2d-c53b-481f-b825-e3f328ea46a6","cardType":"basic","front":"What restriction is required when solving $|f(x)|=g(x)$?","back":"The right-hand side must satisfy $g(x)\\ge 0$.","points":1,"mcqOptions":null},{"id":"b3aaa0bb-343a-45d2-84ca-76cadddce55f","cardType":"basic","front":"Why must solutions found by squaring a modulus equation be checked?","back":"Squaring can introduce extraneous solutions.","points":2,"mcqOptions":null},{"id":"138234c9-49d8-42f6-98dc-d4178363e2a0","cardType":"cloze","front":"For $k>0$, $|x-a|$\\text{[...]}$.","back":"For $k>0$, $|x-a|$\\boxed{a-k.","points":null,"mcqOptions":null},{"id":"2b512693-c754-4521-b67c-ceffbe812075","car

1.3.6 The modulus function (A-level only) Flashcards

1.3.6 The modulus function (A-level only) Flashcards