You are given the equation $y=\\simplify[all,fractionNumbers]{{a}x+{b}}$.
", "preamble": {"css": "", "js": ""}, "parts": [{"showCellAnswerState": true, "useCustomName": false, "prompt": "This equation, or its graph, can be described as a
", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "distractors": ["", "", "", "", "", ""], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["straight line
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", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "As we move to the far left of the graph, the graph
", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["goes upwards.
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\nThe leading term (the term that includes the highest power) determines the long term behaviour of a polynomial. In our polynomial the leading term is $\\simplify[all,fractionNumbers]{{a}x}$.
\nAs we go far to the left of the graph $x$ is negative, and so $\\simplify[all,fractionNumbers]{{a}x}$ is negative. That is, the graph goes downwards. is positive. That is, the graph goes upwards.
\n", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"showCellAnswerState": true, "useCustomName": false, "prompt": "As we move to the far right of the graph, the graph
", "scripts": {}, "showCorrectAnswer": true, "unitTests": [], "showFeedbackIcon": true, "stepsPenalty": "1", "maxMarks": 0, "displayType": "radiogroup", "minMarks": 0, "choices": ["goes upwards.
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\nThe leading term (the term that includes the highest power) determines the long term behaviour of a polynomial. In our polynomial the leading term is $\\simplify[all,fractionNumbers]{{a}x}$.
\nAs we go far to the right of the graph $x$ is positive, and so $\\simplify[all,fractionNumbers]{{a}x}$ is negative. That is, the graph goes downwards. is positive. That is, the graph goes upwards.
\n", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "type": "1_n_2", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": true, "minValue": "{b}", "marks": 1, "maxValue": "{b}", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": true, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "The $y$-intercept is the value of $y$ when $x=0$, that is, the value of $y$ where the graph hits the $y$-axis. To find it, substitute $x=0$ into our equation:
\n\\[y=\\simplify[unitFactor,basic,fractionNumbers]{{a}0+{b}}=\\var{b}.\\]
\n", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "The $y$-intercept of the graph is $y=$[[0]].
", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"checkingType": "absdiff", "checkVariableNames": false, "valuegenerators": [], "useCustomName": false, "vsetRange": [0, 1], "checkingAccuracy": 0.001, "unitTests": [], "showFeedbackIcon": true, "answer": "set({xints})", "scripts": {}, "failureRate": 1, "showPreview": true, "showCorrectAnswer": true, "marks": 1, "vsetRangePoints": 5, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "jme", "customMarkingAlgorithm": ""}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "Round your decimal to three decimal places.
\nThe $x$-intercept is the value of $x$ when $y=0$, that is, the value of $x$ where the graph hits the $x$-axis. To find it, substitute $y=0$ into our equation:
\n\\[0=\\simplify[all,fractionNumbers]{{a}x+{b}} \\]
\n\nSolving this equation tells us that the $x$-intercept is $x=\\simplify[all, fractionNumbers]{{-b}/{a}}$.
", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "The set of $x$-intercepts of the graph would be [[0]].
\nNote: If there are no intercepts, enter set()
\nIf there is only one intercept, say $x=5$, enter set(5)
\nIf there are two intercepts, say $x=-2$ and $x=1.5$, enter set(-2,1.5)
\nIf there are three intercepts, say $x=-2$, $x=1.5$ and $x=5$, enter set(-2,1.5,5)
\n", "unitTests": [], "scripts": {}, "type": "gapfill", "customMarkingAlgorithm": ""}, {"sortAnswers": false, "marks": 0, "gaps": [{"mustBeReduced": false, "useCustomName": false, "notationStyles": ["plain", "en", "si-en"], "showFractionHint": true, "showCorrectAnswer": true, "unitTests": [], "mustBeReducedPC": 0, "showFeedbackIcon": true, "scripts": {}, "correctAnswerFraction": false, "minValue": "0", "marks": 1, "maxValue": "0", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "allowFractions": false, "customName": "", "adaptiveMarkingPenalty": 0, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "customMarkingAlgorithm": "", "correctAnswerStyle": "plain"}], "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "steps": [{"marks": 0, "useCustomName": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "A degree $n$ polynomial has at most $n-1$ bends in its graph.
", "unitTests": [], "scripts": {}, "type": "information", "customMarkingAlgorithm": ""}], "customName": "", "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "prompt": "Given the degree of a polynomial is $1$, the maximum number of possible 'bends' or 'turns' in the graph is [[0]].
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