2a:null 2b:["$","title",null,{"children":"The power function | Mattias Villani | Observable"}] 31:[] 2e:{"id":"c89565a04c2afa05","slug":"the-power-function","title":"The power function","thumbnail":"f8f1baa18714aa803bc15b829a921f61ca98392a144b71d37aa4b821e0ed1633","access_level":"public","create_time":"$D2025-03-13T13:42:09.240Z","update_time":"$D2025-03-13T18:32:30.705Z","view_time":null,"first_public_time":"$D2025-03-13T15:39:30.006Z","fork":{"id":"b3fedb483c609af0","slug":"the-exponential-function","title":"The exponential function","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"stars":0,"starred":false,"owner":{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024"},"version":150,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null}],"members":[{"type":"individual","id":"56499be8cf43f0ef","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":null,"role":"editor"},{"type":"team","id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani","avatar_url":"https://avatars-next.observableusercontent.com/a440aaf39a3abefb86cbcc758fd7a5ab42555ae68d6825b52ec006f385a94d1d","tier":"pro_2024","role":"viewer"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"10fcfcb3f60db359","slug":"basic-maths","title":"Basic Mathematics","owner":{"id":"7592a7ab121f74a0","login":"mattiasvillani","name":"Mattias Villani"}},"type":"notebook","body":{"title":"The power function","cells":[{"id":4,"value":"# The power function","pinned":false,"hidden":false,"mode":"md"},{"id":29,"value":"A [power function](https://en.wikipedia.org/wiki/Exponentiation#Power_functions) is of the form\n${tex.block`f(x)=c x^a`}\nfor some real numbers ${tex`c`} and ${tex`a`}.","pinned":false,"hidden":false,"mode":"md"},{"id":6,"value":"viewof inputs = Inputs.form({\n c: Inputs.range([0, 5], {value: 1, step: 0.1, label: \"c\"}),\n a: Inputs.range([-5, 5], {value: 1, step: 0.1, label: \"a\"}),\n})\n ","pinned":false,"hidden":false,"mode":"ojs"},{"id":7,"value":"Plot.plot({\n title: \"The power function\",\n style: \"font-size: 12px;\",\n x: {\n label: \"x\",\n //domain: xdomain \n },\n y: {\n label: \"f(x)\",\n //domain: [0, Math.exp(xdomain[1])],\n },\n marks: [\n Plot.ruleY([0]),\n Plot.ruleX([0]),\n Plot.line(funcdata, {x: \"x\", y: \"y\", stroke: colors[2], strokeWidth: 3})\n ]\n})","pinned":false,"hidden":false,"mode":"ojs"},{"id":14,"value":"
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\n\n---\n## 🙈 Appendix 🙈\n\nHere is some code and data details that you probably do not want to read.","pinned":false,"hidden":false,"mode":"md"},{"id":16,"value":"#### Imports","pinned":false,"hidden":false,"mode":"md"},{"id":18,"value":"import {colors} from \"@mattiasvillani/statistics-tools\"","pinned":true,"hidden":false,"mode":"ojs"},{"id":20,"value":"mathjs = require('mathjs')","pinned":false,"hidden":false,"mode":"ojs"},{"id":23,"value":"#### Data","pinned":false,"hidden":false,"mode":"md"},{"id":25,"value":"function f(x, c, a){\n const useLogForm = true\n if (useLogForm){\n return c*Math.exp(a*Math.log(x))\n }else{\n return c*x**a\n }\n}","pinned":false,"hidden":false,"mode":"ojs"},{"id":40,"value":"xdomain = [0,5]","pinned":false,"hidden":false,"mode":"ojs"},{"id":36,"value":"funcdata = {\n return d3.range(xdomain[0], xdomain[1], (xdomain[1] - xdomain[0])/1000).map(d => ({x: d, y: f(d, inputs.c, inputs.a)}))\n}","pinned":true,"hidden":false,"mode":"ojs"}],"files":"$W31","stdlib":"1","titling":"auto"}} 2f:"$2e:body"