{"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 $G(A)$ and the $y$-axis, which is the point on the graph where $A=0$. \n\nThe $y$-intercept in this graph is $(0,1.4)$, which means that *at sea level, the tree grows by $\\textit{1.4}$ millimeters each year.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by one and is labeled A for the altitude which is measured in kilometers above sea level. The y-axis scales by zero point two and is labeled G of A for the growth rate of the tree. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, one point four. It increases through the point two, two and the point five, two point five until it reach a local maximum at seven, two point six. Then it decreases through the point nine, two point five, the point twelve, two, and the point fourteen, one point four. The y-intercept zero, one point four is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/49b14000a37e2dd3c5d2c21be4b4721d983d459c", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"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 maximum point where $G(A)=2.6$, which means that *the fastest possible growth rate is $\\textit{2.6}$ millimeters per year.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by one and is labeled A for the altitude which is measured in kilometers above sea level. The y-axis scales by zero point two and is labeled G of A for the growth rate of the tree. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, one point four. It increases through the point two, two and the point five, two point five until it reach a local maximum at seven, two point six. Then it decreases through the point nine, two point five, the point twelve, two, and the point fourteen, one point four. The point seven, two point six is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/c3dcdd44cf5db8b5f48ce2f2317aeac594d296ec", "width": 231}, "box": [231, 231], "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 $[7,14]$ is a decreasing interval. This means that *as the altitude surpasses $\\textit{7}$ kilometers above sea level, the growth rate of the tree declines.*\n\n\n\n[[☃ image 1]]\n\n", "images": {}, "replace": false, "widgets": {"image 1": {"alignment": "block", "graded": true, "options": {"alt": "The first quadrant of a coordinate plane. The x-axis scales by one and is labeled A for the altitude which is measured in kilometers above sea level. The y-axis scales by zero point two and is labeled G of A for the growth rate of the tree. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, one point four. It increases through the point two, two and the point five, two point five until it reach a local maximum at seven, two point six. Then it decreases through the point nine, two point five, the point twelve, two, and the point fourteen, one point four. The function is highlighted from x equals seven to x equals fourteen.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/b9b2d1ea995564b33b14b03173c0f98dae5d9adb", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$y$-intercept | At sea level, the tree grows by $1.4$ millimeters each year.\nRelative maximum or minimum | The fastest possible growth rate is $2.6$ millimeters per year.\nIncreasing or decreasing interval | As the altitude surpasses $7$ kilometers above sea level, the growth rate of the tree declines.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "The altitude of a tree affects the rate at which the tree grows.\n\n$G(A)$ models the growth rate (in millimeters per year) of a certain kind of tree at an altitude $A$ (in kilometers above sea level).\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 quadrant of a coordinate plane. The x-axis scales by zero point five and is labeled A for the altitude which is measured in kilometers above sea level. The y-axis scales by zero point one and is labeled G of A for the growth rate of the tree. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, one point four. It increases through the point two, two and the point five, two point five until it reach a local maximum at seven, two point six. Then it decreases through the point nine, two point five, the point twelve, two, and the point fourteen, one point four.", "backgroundImage": {"height": 464, "url": "web+graphie:${☣ LOCALPATH}/images/698a9789bf3f4961c860cf3c7a72cd9dd448794f", "width": 464}, "box": [464, 464], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$y$-intercept", "Relative maximum or minimum", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["At sea level, the tree grows by $1.4$ millimeters each year.", "The fastest possible growth rate is $2.6$ millimeters per year.", "As the altitude surpasses $7$ kilometers above sea level, the growth rate of the tree declines."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}