{"answerArea": {"calculator": false, "chi2Table": false, "periodicTable": false, "tTable": false, "zTable": false}, "hints": [{"content": "The $y$-intercept is the point of intersection between the graph of the function $T(t)$ and the $y$-axis, which is the point on the graph where $t=0$. \n\nThe $y$-intercept in this graph is $(0,-3)$, which means that *it was $\\textit{-3}\\,^\\circ\\textit{C}$ at the beginning of the day.*\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 hours after midnight. The y-axis scales by one and is labeled T of t for the temperature, in degrees Celsius, of New York City. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, negative three. Then it decreases to the a local minimum at two, negative three point five. It increases through the point five, negative two point five, the x-intercept eight, zero, and the point eleven, one point seven-five until a local maximum at fourteen, two point five. Then it decreases though the point eighteen, one point two-five and the x-intercept twenty, zero. The y-intercept zero, negative three is plotted on the function.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/dc50e92e821bc10d219b0b8f6dcfc3ddef733cf3", "width": 211}, "box": [211, 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 $T(t)>0$ over the interval $[8,20]$, this is a positive interval. This means that *the temperature was above zero between $\\textit{8 am}$ and $\\textit{8 pm}$.*\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 hours after midnight. The y-axis scales by one and is labeled T of t for the temperature, in degrees Celsius, of New York City. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, negative three. Then it decreases to the a local minimum at two, negative three point five. It increases through the point five, negative two point five, the x-intercept eight, zero, and the point eleven, one point seven-five until a local maximum at fourteen, two point five. Then it decreases though the point eighteen, one point two-five and the x-intercept twenty, zero. The function is highlighted from x equals eight to x equals twenty.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/fa9c2d28c78f2dd7b1f1060eadc1a46ce96fab19", "width": 214}, "box": [214, 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 $[2,14]$ is an increasing interval. This means that *it was getting warmer between $\\textit{2 am}$ and $\\textit{2 pm}$.*\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 hours after midnight. The y-axis scales by one and is labeled T of t for the temperature, in degrees Celsius, of New York City. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, negative three. Then it decreases to the a local minimum at two, negative three point five. It increases through the point five, negative two point five, the x-intercept eight, zero, and the point eleven, one point seven-five until a local maximum at fourteen, two point five. Then it decreases though the point eighteen, one point two-five and the x-intercept twenty, zero. The function is highlighted from x equals two to x equals fourteen.", "backgroundImage": {"height": 214, "url": "web+graphie:${☣ LOCALPATH}/images/1636a43d2efa3aca2cb5cde4ec9cf71aa75506ad", "width": 214}, "box": [214, 214], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$y$-intercept | It was $-3^\\circ\\text{C}$ at the beginning of the day.\nPositive or negative interval | The temperature was above zero between $8\\text{ am}$ and $8\\text{ pm}$.\nIncreasing or decreasing interval | It was getting warmer between $2\\text{ am}$ and $2\\text{ pm}$.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "$T(t)$ models the temperature (in degrees Celsius) in New York City when it's $t$ hours after midnight on a given day.\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 hours after midnight. The y-axis scales by zero point five and is labeled T of t for the temperature, in degrees Celsius, of New York City. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, negative three. Then it decreases to the a local minimum at two, negative three point five. It increases through the point five, negative two point five, the x-intercept eight, zero, and the point eleven, one point seven-five until a local maximum at fourteen, two point five. Then it decreases though the point eighteen, one point two-five and the x-intercept twenty, zero.", "backgroundImage": {"height": 440, "url": "web+graphie:${☣ LOCALPATH}/images/4584cddc325add7c6a47f9dfa5b0c0c22cf335e6", "width": 464}, "box": [464, 440], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$y$-intercept", "Positive or negative interval", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["It was $-3^\\circ\\text{C}$ at the beginning of the day.", "The temperature was above zero between $8\\text{ am}$ and $8\\text{ pm}$.", "It was getting warmer between $2\\text{ am}$ and $2\\text{ pm}$."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}