// Numbas version: exam_results_page_options
{"name": "22-23 CLE W2 Q5 Sketching graphs: transformations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "22-23 CLE W2 Q5 Sketching graphs: transformations", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>The following questions ask you to explore the transformation of each function.</p>", "advice": "<p>In part a), a vertical shift (i.e., translation) is always indicated by $f(x) \\pm$ shift-factor.</p>\n<p>In part b), horizontal translations are often indicated within brackets. For example, something like $f(x-2)$ would indicate a translation of $+2$ parallel to the $x-$axis. Note that the sign of the shift-factor is usually \"opposite\" to the direction of the actual shift itself.</p>\n<p>For part c), the $y-$intercept can be found by setting $x=0$ and observing what the fuctions returns. However, the function itself will undergo a vertical \"stretch\" or \"squash\" if the function is multiplied by a shift-factor. In any case, if you are unsure then try to sketch the transformed function and physically visualise where the $y-$intercept will be.</p>\n<p>In part d), the same advice for part c) holds. Try to sketch the function using your knowledge of graph translations in order to find the $y-$intercept here.</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5,-4,-3,-2,-1,1,2,3,4,5)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": false, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $f(x)=\\frac{1}{x}$, where $x \\neq 0$, which of the following functions shifts the graph vertically by $\\var{a}$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$y=f(x)+\\var{a}$", "$y=f(\\var{a}x)$", "$y=\\var{a}f(x)$", "$y=f(x+\\var{a})$"], "matrix": ["0.25", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Consider the graph of the function $f(x) = 2x^{3}-2x$. How does it compare to the graph of the function $g(x) = 2(x-2)^{3}-2(x-2)$?</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["g(x) is translated +2 parallel to the x-axis (compared to f(x))", "g(x) is translated -2 parallel to the x-axis (compared to f(x))", "g(x) is stretched by a factor of 2 parallel to the y-axis (compared to f(x))", "g(x) is shrunk by a factor of 2 parallel to the y-axis (compared to f(x))"], "matrix": ["0.25", 0, 0, 0], "distractors": ["", "", "", ""]}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>If $f(x)= \\frac{1}{(x+1)^2}$, what is the y-intercept of $y=2f(x)$?</p>\n<p></p>\n<p>y-intercept = [[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": true, "customName": "y-intercept", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["(2,0)", "(0,2)", "(4,0)", "(0,4)"], "matrix": [0, "0.25", 0, 0], "distractors": ["", "", "", ""]}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given that $f(x)=\\frac{1}{x^{2}}$, what is the y-intercept of $y=f(x+2)$?</p>\n<p></p>\n<p>y-intercept = [[0]]</p>", "gaps": [{"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "radiogroup", "displayColumns": 0, "showCellAnswerState": true, "choices": ["$(\\frac{1}{2},0)$", "$(0,\\frac{1}{2})$", "$(\\frac{1}{4},0)$", "$(0,\\frac{1}{4})$"], "matrix": [0, 0, 0, "0.25"], "distractors": ["", "", "", ""]}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Hannah Lerman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9851/"}, {"name": "Nahid Chowdhury", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18252/"}]}]}], "contributors": [{"name": "Hannah Lerman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/9851/"}, {"name": "Nahid Chowdhury", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/18252/"}]}