{
  localUrl: '../page/function_image.html',
  arbitalUrl: 'https://arbital.com/p/function_image',
  rawJsonUrl: '../raw/3lh.json',
  likeableId: '2491',
  likeableType: 'page',
  myLikeValue: '0',
  likeCount: '1',
  dislikeCount: '0',
  likeScore: '1',
  individualLikes: [
    'EricRogstad'
  ],
  pageId: 'function_image',
  edit: '7',
  editSummary: '',
  prevEdit: '6',
  currentEdit: '7',
  wasPublished: 'true',
  type: 'wiki',
  title: 'Image (of a function)',
  clickbait: '',
  textLength: '1180',
  alias: 'function_image',
  externalUrl: '',
  sortChildrenBy: 'likes',
  hasVote: 'false',
  voteType: '',
  votesAnonymous: 'false',
  editCreatorId: 'NateSoares',
  editCreatedAt: '2016-06-10 16:45:50',
  pageCreatorId: 'NateSoares',
  pageCreatedAt: '2016-05-13 23:17:23',
  seeDomainId: '0',
  editDomainId: 'AlexeiAndreev',
  submitToDomainId: '0',
  isAutosave: 'false',
  isSnapshot: 'false',
  isLiveEdit: 'true',
  isMinorEdit: 'false',
  indirectTeacher: 'false',
  todoCount: '0',
  isEditorComment: 'false',
  isApprovedComment: 'true',
  isResolved: 'false',
  snapshotText: '',
  anchorContext: '',
  anchorText: '',
  anchorOffset: '0',
  mergedInto: '',
  isDeleted: 'false',
  viewCount: '66',
  text: 'The image $\\operatorname{im}(f)$ of a [3jy function] $f : X \\to Y$ is the set of all possible outputs of $f$, which is a subset of $Y$. Using [3lj set builder notation], $\\operatorname{im}(f) = \\{f(x) \\mid x \\in X\\}.$\n\nVisualizing a function as a map that takes every point in an input set to one point in an output set, the image is the set of all places where $f$-arrows land (pictured as the yellow subset of $Y$ in the image below).\n\n![Domain, Codomain, and Image](http://i.imgur.com/ZZgVHaI.png)\n\nThe image of a function is not to be confused with the [3lg codomain], which is the _type_ of output that the function produces. For example, consider the [43x Ackermann function], which is a very fast-growing (and difficult to compute) function. When someone asks what sort of thing the Ackermann function produces, the natural answer is not "something from a sparse and hard-to-calculate set of numbers that I can't tell you off the top of my head"; the natural answer is "it outputs a number." In this case, the codomain is "number", while the image is the sparse and hard-to-calculate subset of numbers. For more on this distinction, see the page on [3lv codomain vs image].',
  metaText: '',
  isTextLoaded: 'true',
  isSubscribedToDiscussion: 'false',
  isSubscribedToUser: 'false',
  isSubscribedAsMaintainer: 'false',
  discussionSubscriberCount: '1',
  maintainerCount: '1',
  userSubscriberCount: '0',
  lastVisit: '',
  hasDraft: 'false',
  votes: [],
  voteSummary: 'null',
  muVoteSummary: '0',
  voteScaling: '0',
  currentUserVote: '-2',
  voteCount: '0',
  lockedVoteType: '',
  maxEditEver: '0',
  redLinkCount: '0',
  lockedBy: '',
  lockedUntil: '',
  nextPageId: '',
  prevPageId: '',
  usedAsMastery: 'false',
  proposalEditNum: '0',
  permissions: {
    edit: {
      has: 'false',
      reason: 'You don't have domain permission to edit this page'
    },
    proposeEdit: {
      has: 'true',
      reason: ''
    },
    delete: {
      has: 'false',
      reason: 'You don't have domain permission to delete this page'
    },
    comment: {
      has: 'false',
      reason: 'You can't comment in this domain because you are not a member'
    },
    proposeComment: {
      has: 'true',
      reason: ''
    }
  },
  summaries: {},
  creatorIds: [
    'NateSoares'
  ],
  childIds: [
    'codomain_vs_image'
  ],
  parentIds: [
    'function'
  ],
  commentIds: [
    '3lp'
  ],
  questionIds: [],
  tagIds: [
    'needs_clickbait_meta_tag',
    'definition_meta_tag'
  ],
  relatedIds: [],
  markIds: [],
  explanations: [],
  learnMore: [],
  requirements: [],
  subjects: [],
  lenses: [],
  lensParentId: '',
  pathPages: [],
  learnMoreTaughtMap: {},
  learnMoreCoveredMap: {},
  learnMoreRequiredMap: {},
  editHistory: {},
  domainSubmissions: {},
  answers: [],
  answerCount: '0',
  commentCount: '0',
  newCommentCount: '0',
  linkedMarkCount: '0',
  changeLogs: [
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '17151',
      pageId: 'function_image',
      userId: 'EricBruylant',
      edit: '0',
      type: 'newTag',
      createdAt: '2016-07-19 02:20:46',
      auxPageId: 'needs_clickbait_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '12339',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '7',
      type: 'newEdit',
      createdAt: '2016-06-10 16:45:50',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10310',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '6',
      type: 'newEdit',
      createdAt: '2016-05-14 05:12:34',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10308',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '5',
      type: 'newEdit',
      createdAt: '2016-05-14 04:33:41',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10307',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '4',
      type: 'newEdit',
      createdAt: '2016-05-14 01:43:47',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10299',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '3',
      type: 'newChild',
      createdAt: '2016-05-14 01:37:54',
      auxPageId: 'codomain_vs_image',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10295',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '3',
      type: 'newEdit',
      createdAt: '2016-05-14 01:02:59',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10249',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '2',
      type: 'newEdit',
      createdAt: '2016-05-13 23:26:18',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10243',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '1',
      type: 'newEdit',
      createdAt: '2016-05-13 23:17:23',
      auxPageId: '',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10240',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '1',
      type: 'newParent',
      createdAt: '2016-05-13 23:17:06',
      auxPageId: 'function',
      oldSettingsValue: '',
      newSettingsValue: ''
    },
    {
      likeableId: '0',
      likeableType: 'changeLog',
      myLikeValue: '0',
      likeCount: '0',
      dislikeCount: '0',
      likeScore: '0',
      individualLikes: [],
      id: '10239',
      pageId: 'function_image',
      userId: 'NateSoares',
      edit: '1',
      type: 'newTag',
      createdAt: '2016-05-13 23:17:04',
      auxPageId: 'definition_meta_tag',
      oldSettingsValue: '',
      newSettingsValue: ''
    }
  ],
  feedSubmissions: [],
  searchStrings: {},
  hasChildren: 'true',
  hasParents: 'true',
  redAliases: {},
  improvementTagIds: [],
  nonMetaTagIds: [],
  todos: [],
  slowDownMap: 'null',
  speedUpMap: 'null',
  arcPageIds: 'null',
  contentRequests: {
    fewerWords: {
      likeableId: '3687',
      likeableType: 'contentRequest',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '140',
      pageId: 'function_image',
      requestType: 'fewerWords',
      createdAt: '2016-11-04 11:22:08'
    },
    moreTechnical: {
      likeableId: '3688',
      likeableType: 'contentRequest',
      myLikeValue: '0',
      likeCount: '1',
      dislikeCount: '0',
      likeScore: '1',
      individualLikes: [],
      id: '141',
      pageId: 'function_image',
      requestType: 'moreTechnical',
      createdAt: '2016-11-04 11:22:27'
    }
  }
}