Flashcards","topicId":"a856e5bd-668a-4878-a60e-6fbd09b90bad","topicSlug":"algebra-and-functions-14","cards":[{"id":"595ba868-8e95-44c9-a909-771c51c3ff32","cardType":"cloze","front":"Every point on a graph has coordinates that [ ].","back":"Every point on a graph has coordinates that satisfy the graph's equation.","points":null,"mcqOptions":null},{"id":"38655a45-0aa5-43e4-9a18-ca25ae61a0ef","cardType":"basic","front":"Why does $(2,5)$ lie on $y=x^2+1$?","back":"Substitution gives $5=2^2+1$.","points":2,"mcqOptions":null},{"id":"a6aa5961-0d6f-4f87-b68b-b6b9f36acd25","cardType":"cloze","front":"At an intersection, the coordinates satisfy [ ].","back":"At an intersection, the coordinates satisfy both graph equations simultaneously.","points":null,"mcqOptions":null},{"id":"676aa3aa-e391-4514-9bef-98687dc3bfc8","cardType":"cloze","front":"The solutions of $f(x)=g(x)$ are the [ ] of the intersections of $y=f(x)$ and $y=g(x)$.","back":"The solutions of $f(x)=g(x)$ are the $x$-coordinates of the intersections of $y=f(x)$ and $y=g(x)$.","points":null,"mcqOptions":null},{"id":"9e20edcc-f975-47b3-92f1-4d4be2dea8f7","cardType":"basic","front":"The graphs for $x^2-2=2$ intersect at $(-2,2)$ and $(2,2)$. What are the solutions?","back":"$x=-2$ or $x=2$.","points":1,"mcqOptions":null},{"id":"a2c2def8-e5da-40dd-95d7-34ecee4fc80c","cardType":"cloze","front":"A root of $f$ is a value of $x$ for which $\\text{[...]}$.","back":"A root of $f$ is a value of $x$ for which $\\boxed{f(x)=0}$.","points":null,"mcqOptions":null},{"id":"da744eb9-6ed6-4bb6-8c2b-429028d7c517","cardType":"cloze","front":"Graphically, roots are the $x$-coordinates where $y=f(x)$ meets the [ ].","back":"Graphically, roots are the $x$-coordinates where $y=f(x)$ meets the $x$-axis.","points":null,"mcqOptions":null},{"id":"a8a8264c-2205-4cca-9388-4e08ef000860","cardType":"basic","front":"A graph of $y=f(x)$ crosses the $x$-axis at $x=-3$, $1$ and $4$. Solve $f(x)=0$.","back":"$x=-3,\\,1,\\,4$.","points":1,"mcqOptions":null},{"id":"479ad3a6-0729-4819-9e71-4099ace39d95","cardType":"basic","front":"Which two graphs can solve $x^2-3x-1=0$ after rearranging to $x^2=3x+1$?","back":"$y=x^2$ and $y=3x+1$.","points":2,"mcqOptions":null},{"id":"09bd95cb-2630-47d6-97a3-ecf368ee6816","cardType":"basic","front":"How can $x^2-3x-1=0$ instead be solved using one curve and the $x$-axis?","back":"Intersect $y=x^2-3x-1$ with $y=0$.","points":2,"mcqOptions":null},{"id":"43369c02-b6a7-4ddf-a3b0-594dc0eb160f","cardType":"basic","front":"After rewriting $x^3-2x=5$ as $x^3=2x+5$, which graphs should be intersected?","back":"$y=x^3$ and $y=2x+5$.","points":2,"mcqOptions":null},{"id":"a7e7ccb4-57a2-4afd-848d-4b2ebd9bf742","cardType":"basic","front":"Why does a touching point still give a solution to $f(x)=g(x)$?","back":"Both graphs have the same $y$-value at the same $x$.","points":2,"mcqOptions":null},{"id":"bc6fb0fa-aa5a-4cc3-9bc9-d4aeaca308a0","cardType":"basic","front":"What follows if a quadratic graph touches the $x$-axis once?","back":"It has one repeated real root.","points":1,"mcqOptions":null},{"id":"64b37f85-bfc1-43aa-9ec1-cbd3c1b5f465","cardType":"cloze","front":"If $y=f(x)$ and $y=g(x)$ intersect twice, $f(x)=g(x)$ has [ ].","back":"If $y=f(x)$ and $y=g(x)$ intersect twice, $f(x)=g(x)$ has two real solutions.","points":null,"mcqOptions":null},{"id":"12209ec0-14b1

1.1.13 Algebra and functions Flashcards

1.1.13 Algebra and functions Flashcards