{"answerArea": {"calculator": false, "chi2Table": false, "periodicTable": false, "tTable": false, "zTable": false}, "hints": [{"content": "A relative maximum (or minimum) point is a point that is higher (or lower) than all of the points surrounding it.\n\nThis graph has a relative minimum point at $t=6$, which means that *the gym's net worth was at its lowest at $\\textit{6}$ months.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by two and is labeled t for the number of months. The y-axis scales by two and is labeled N of t for the net worth of the gym in thousands of dollars. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, four, then it decreases through the x-intercept zero, two and the point four, negative two point five until it reaches a local minimum at six, negative three. Then it increases through the point eight, negative two point five, the x-intercept ten, zero, and the point twelve point. The point six, zero is plotted.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/c15b3321e7f8eee33b2d0dba9bd2516f76d9a2a9", "width": 221}, "box": [221, 214], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "A positive (or negative) interval is a domain interval over which the function values are all positive (or negative).\n\nSince $N(t)<0$ over the interval $[2,10]$, this is a negative interval. This means that *the gym's losses exceeded its profits between $\\textit{2}$ and $\\textit{10}$ months after opening.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by two and is labeled t for the number of months. The y-axis scales by two and is labeled N of t for the net worth of the gym in thousands of dollars. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, four, then it decreases through the x-intercept zero, two and the point four, negative two point five until it reaches a local minimum at six, negative three. Then it increases through the point eight, negative two point five, the x-intercept ten, zero, and the point twelve point. The function is highlighted from x equals two to x equals ten.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/8b7a7cc18d60e197ed6828bf9e595dffdf414efe", "width": 221}, "box": [221, 214], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "An increasing (or decreasing) interval is a domain interval over which the function values increase (or decrease) as the input variable increases.\n\nIn this graph, the interval $[0,6]$ is a decreasing interval. This means that *the gym was losing money for the first $\\textit{6}$ months.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by two and is labeled t for the number of months. The y-axis scales by two and is labeled N of t for the net worth of the gym in thousands of dollars. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, four, then it decreases through the x-intercept zero, two and the point four, negative two point five until it reaches a local minimum at six, negative three. Then it increases through the point eight, negative two point five, the x-intercept ten, zero, and the point twelve point. The function is highlighted from x equals zero to x equals six.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/deb7dced41e2d7ae7bca09822270221260119b27", "width": 221}, "box": [221, 214], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\nRelative maximum or minimum | The gym's net worth was at its lowest at $6$ months.\nPositive or negative interval | The gym's losses exceeded its profits between $2$ and $10$ months after opening.\nIncreasing or decreasing interval | The gym was losing money for the first $6$ months.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Sabin opened a new martial arts gym.\n\n$N(t)$ models the net worth of the gym (in thousands of dollars) after $t$ months.\n\n**Match each statement with the feature of the graph that most closely corresponds to it.**\n\n\n\n[[☃ image 1]]\n\n[[☃ matcher 1]]", "images": {}, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first and fourth quadrants of a coordinate plane. The x-axis scales by one and is labeled t for the number of months. The y-axis scales by one and is labeled N of t for the net worth of the gym in thousands of dollars. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, four, then it decreases through the x-intercept zero, two and the point four, negative two point five until it reaches a local minimum at six, negative three. Then it increases through the point eight, negative two point five, the x-intercept ten, zero, and the point twelve, four.", "backgroundImage": {"height": 448, "url": "web+graphie:${☣ LOCALPATH}/images/588507fcfaa9a18dca6a79ad52b3142c8a9e7a20", "width": 464}, "box": [464, 448], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["Relative maximum or minimum", "Positive or negative interval", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["The gym's net worth was at its lowest at $6$ months.", "The gym's losses exceeded its profits between $2$ and $10$ months after opening.", "The gym was losing money for the first $6$ months."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}