n points of graphs Flashcards","topicId":"4f678fb8-7570-4290-8bca-24219f2672c3","topicSlug":"intersection-points-of-graphs","cards":[{"id":"9c1a07b4-113a-45b8-96f5-503569099546","cardType":"basic","front":"Why does $(2,5)$ lie on $y=2x+1$?","back":"Substituting $x=2$ gives $y=5$.","points":2,"mcqOptions":null},{"id":"81c16ec6-2c41-4f96-b51a-48a5339f072c","cardType":"basic","front":"Why does an intersection point solve two equations simultaneously?","back":"Its coordinates satisfy both equations.","points":2,"mcqOptions":null},{"id":"62aa06d3-4c13-4db0-94b3-251cab0934eb","cardType":"cloze","front":"At an intersection of $y=f(x)$ and $y=g(x)$, $\\text{[...]}$.","back":"At an intersection of $y=f(x)$ and $y=g(x)$, $\\boxed{f(x)=g(x)}$.","points":null,"mcqOptions":null},{"id":"ad8d48df-1581-49b2-a943-c2771af4ab06","cardType":"basic","front":"After finding an intersection's $x$-coordinate, how is its $y$-coordinate found?","back":"Substitute $x$ into either original equation.","points":1,"mcqOptions":null},{"id":"c615af7e-cf20-413b-955a-2fc6081c0c4e","cardType":"cloze","front":"Intersections with the $x$-axis satisfy $\\text{[...]}$.","back":"Intersections with the $x$-axis satisfy $\\boxed{f(x)=0}$.","points":null,"mcqOptions":null},{"id":"1202c641-b649-443a-a83a-dc670ba1b765","cardType":"basic","front":"What three names are given to the solutions of $f(x)=0$?","back":"

Roots
Zeros
Solutions

","points":3,"mcqOptions":null},{"id":"497ad7c1-490d-4c85-8f1c-8de0a83299ef","cardType":"cloze","front":"The $y$-intercept of $y=f(x)$ is found by calculating $\\text{[...]}$.","back":"The $y$-intercept of $y=f(x)$ is found by calculating $\\boxed{f(0)}$.","points":null,"mcqOptions":null},{"id":"e09cc974-a048-421f-92aa-5346aba6ace1","cardType":"basic","front":"What are the $x$-axis intersections of $y=x^3-4x$?","back":"$(-2,0)$, $(0,0)$ and $(2,0)$.","points":3,"mcqOptions":null},{"id":"4d9ade94-4fd0-4332-9a77-cd986912246a","cardType":"basic","front":"Which two graphs represent the equation $\\sqrt{x+1}=3-x$?","back":"

$y=\\sqrt{x+1}$
$y=3-x$

","points":2,"mcqOptions":null},{"id":"842247ff-90eb-423b-a50c-54f45773a649","cardType":"basic","front":"Which coordinates of the intersections of $y=f(x)$ and $y=g(x)$ solve $f(x)=g(x)$?","back":"The $x$-coordinates.","points":1,"mcqOptions":null},{"id":"c4f58d37-472b-458b-a3cd-9357fac18875","cardType":"basic","front":"What interval can contain solutions of $\\sqrt{x+1}=3-x$?","back":"$-1\\leq x\\leq 3$.","points":1,"mcqOptions":null},{"id":"81d08c36-2618-4b00-b35d-dcbf0fbb38f2","cardType":"basic","front":"Why is $\\frac{7+\\sqrt{17}}{2}$ invalid for $\\sqrt{x+1}=3-x$?","back":"It is greater than $3$, violating the required domain.","points":2,"mcqOptions":null},{"id":"df26e9d6-c064-4596-8336-18e204e4fb7d","cardType":"basic","front":"Why must solutions found after squaring both sides be checked?","back":"Squaring can create extraneous solutions that fail the original equation.","points":2,"mcqOptions":null},{"id":"4319475a-3e62-4c9e-8eb2-27115f747dbc","cardType":"basic","front":"What equation results from substituting $y=x+1$ into $x^2+y^2=13$ and simplifying?","back":"$x^2+x-6=0$.","points":1,"mcqOptions":null},{"id":"96499634-65b9-4bdd-a614-c173c819a15d","cardType":"basic","front":"Where do $y=x+1$ and $x^2+y^2=13$ intersect?","back":"$(-3,-2)$ and $(2,3)$.","points":2,"mcqOptions":null},{"id":"65f67a5d-c6d5-4a87-9693-cf3ee143415e","cardType":"cloze","front":"The number of real solutions of $f(x)=g(x)$ equals the [ ] of their graphs.","back":"The number of real solutions of $f(x)=g(x

1.2.17 Intersection points of graphs Flashcards

1.2.17 Intersection points of graphs Flashcards