nd Functions (A-level only) Flashcards","topicId":"37874f00-9a27-43a4-ba9c-2e0a03089080","topicSlug":"algebra-and-functions-18","cards":[{"id":"cf58b9bd-da00-44b3-950e-0f1d1f96a400","cardType":"basic","front":"When does $(p,q)$ lie on the graph $y=f(x)$?","back":"When $q=f(p)$.","points":1,"mcqOptions":null},{"id":"dfd4532f-6fff-4c37-ba8d-39bd88060d84","cardType":"basic","front":"Which direction is affected by a change outside $f(x)$?","back":"The vertical direction.","points":1,"mcqOptions":null},{"id":"6f1fec5c-9178-44c5-827d-3a6752b25510","cardType":"basic","front":"Which direction is affected by a change inside $f$?","back":"The horizontal direction.","points":1,"mcqOptions":null},{"id":"d52113b4-ce24-4ac7-b5c0-8c543b11606a","cardType":"cloze","front":"In $y=af(x)$, $(p,q)$ maps to $\\text{[...]}$, so the $x$-coordinate is unchanged.","back":"In $y=af(x)$, $(p,q)$ maps to $\\boxed{(p,aq)}$, so the $x$-coordinate is unchanged.","points":null,"mcqOptions":null},{"id":"d7520816-5572-4150-acee-9b42fb532184","cardType":"cloze","front":"In $y=af(x)$, $(p,q)$ maps to $(p,aq)$, so the [ ] is unchanged.","back":"In $y=af(x)$, $(p,q)$ maps to $(p,aq)$, so the $x$-coordinate is unchanged.","points":null,"mcqOptions":null},{"id":"e495b6bf-68b8-4c0e-a462-0438f00ffbe3","cardType":"basic","front":"How does $y=af(x)$ transform the graph when $a>1$?","back":"A vertical stretch with scale factor $a$.","points":1,"mcqOptions":null},{"id":"4750ac0f-fa7f-4c7f-8119-48a68c9876dc","cardType":"basic","front":"What additional transformation occurs in $y=af(x)$ when $a<0$?","back":"A reflection in the $x$-axis.","points":1,"mcqOptions":null},{"id":"6a6c3390-edbb-409f-a175-877ab357a553","cardType":"basic","front":"Where does $(4,5)$ move under $y=-3f(x)+2$?","back":"$(4,-13)$.","points":2,"mcqOptions":null},{"id":"a70b3707-5aeb-42fc-b4bb-184c26eca3d7","cardType":"cloze","front":"Under $y=f(x)+a$, $(p,q)$ maps to $\\text{[...]}$. If $a<0$, the graph moves down by $|a|$ units.","back":"Under $y=f(x)+a$, $(p,q)$ maps to $\\boxed{(p,q+a)}$. If $a<0$, the graph moves down by $|a|$ units.","points":null,"mcqOptions":null},{"id":"99c71d4f-1fb7-4655-82fc-17f31380d92c","cardType":"cloze","front":"Under $y=f(x)+a$, $(p,q)$ maps to $(p,q+a)$. If $a<0$, the graph moves [ ].","back":"Under $y=f(x)+a$, $(p,q)$ maps to $(p,q+a)$. If $a<0$, the graph moves down by $|a|$ units.","points":null,"mcqOptions":null},{"id":"4f9eb90d-8885-468e-bf9b-2d523353f5b9","cardType":"basic","front":"A minimum of $y=f(x)$ is $(3,-4)$. Where is it on $y=f(x)+7$?","back":"$(3,3)$.","points":1,"mcqOptions":null},{"id":"8134b5fd-f1e1-4b33-a799-2f2e11b309ec","cardType":"basic","front":"Where does $(p,q)$ move under $y=f(x+a)$?","back":"$(p-a,q)$.","points":1,"mcqOptions":null},{"id":"236f470b-f1ce-4957-9f14-e3249ebc9428","cardType":"basic","front":"Why does $y=f(x+a)$ translate the graph left when $a>0$?","back":"The old input $p$ occurs when $x+a=p$, so $x=p-a$.","points":2,"mcqOptions":null},{"id":"aaf8f315-413b-443f-8bd5-459bb59edba7","cardType":"basic","front":"The roots of $f(x)$ are $-1$ and $4$. What are the roots of $f(x+3)$?","back":"$-4$ and $1$.","points":2,"mcqOptions":null},{"id":"41ae8970-95fa-4cdf-aed4-da6c0a9772e5","cardType":"cloze","front":"For $y=f(ax)$, the horizontal scale factor is $\\text{[...]}$. For $a>0$, $(p,q)$ maps to $hat(\frac{p}{a},q\right)$.","back":"For $y=f(ax)$, the horizontal scale factor is $\\boxed{rac{1}{|a|}}$. For $a>0$, $(p,q)$ maps to $hat(\frac{p}{a},q\right)$.","points":null,"mcqOptions":null},{"id":"b5528322-8727-40ab-ba52-6746762f170e","cardType":"cloze","front":"For $y=f(ax)$, the horizontal scale factor is $rac{1}{|a|}$. For $a>0$, $(p,q)$ maps to $\\t

3.2.4 Algebra and Functions (A-level only) Flashcards

3.2.4 Algebra and Functions (A-level only) Flashcards