{"answerArea": {"calculator": false, "chi2Table": false, "periodicTable": false, "tTable": false, "zTable": false}, "hints": [{"content": "The $x$-intercept is the point of intersection between the graph of the function $h(d)$ and the $x$-axis, which is the point on the graph where $h(d)=0$. In this case the horizontal axis represents the variable $d$, but it's common to call that axis the $x$-axis.\n\nThis graph has an $x$-intercept at $(90,0)$, which means that *Jan threw the javelin to a distance of $\\textit{90}$ meters.*\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 ten and is labeled d for the horizontal distance in meters. The y-axis scales by four and is labeled h of d for the height of the tip of a javelin in meters. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, five and increases through the point ten, nine, the point twenty, twelve, and the point thirty, thirteen until it reaches a local maximum at forty, fourteen. Then it decreases through the point fifty, thirteen, the point sixty, twelve, the point seventy, nine, and the point eighty, five until it stops at the x-intercept ninety, zero. The point ninety, zero is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/8693a5973a3f0a1e57d3348f63685ebcd32fa4cd", "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 $h(d)=14$, which means that *the highest point the javelin reached was $\\textit{14}$ meters above the ground.*\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 ten and is labeled d for the horizontal distance in meters. The y-axis scales by four and is labeled h of d for the height of the tip of a javelin in meters. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, five and increases through the point ten, nine, the point twenty, twelve, and the point thirty, thirteen until it reaches a local maximum at forty, fourteen. Then it decreases through the point fifty, thirteen, the point sixty, twelve, the point seventy, nine, and the point eighty, five until it stops at the x-intercept ninety, zero. The point forty, fourteen is plotted on the function.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/6d41618a3de1e5baf8dfa162865b0f5e45b2b7ed", "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 $[40,90]$ is a decreasing interval. This means that *the javelin began its descent after the $\\textit{40}$-meter mark.*\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 ten and is labeled d for the horizontal distance in meters. The y-axis scales by four and is labeled h of d for the height of the tip of a javelin in meters. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, five and increases through the point ten, nine, the point twenty, twelve, and the point thirty, thirteen until it reaches a local maximum at forty, fourteen. Then it decreases through the point fifty, thirteen, the point sixty, twelve, the point seventy, nine, and the point eighty, five until it stops at the x-intercept ninety, zero. The function is highlighted from x equals forty to x equals ninety.", "backgroundImage": {"height": 231, "url": "web+graphie:${☣ LOCALPATH}/images/24fdf7046bd3d9af95493c5d082c83770df8ca94", "width": 231}, "box": [231, 231], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}}}, {"content": "To sum it up, the table should look as follows:\n\nFeature | Statement\n:-: | :-:\n$x$-intercept | Jan threw the javelin to a distance of $90$ meters.\nRelative maximum or minimum | The highest point the javelin reached was $14$ meters above the ground.\nIncreasing or decreasing interval | The javelin began its descent after the $40$-meter mark.", "images": {}, "replace": false, "widgets": {}}], "itemDataVersion": {"major": 0, "minor": 1}, "question": {"content": "Jan threw a javelin.\n\n$h(d)$ models the height of the tip of the javelin (in meters) as a function of its horizontal distance (in meters) $d$ from the throwing arc.\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 five and is labeled d for the horizontal distance in meters. The y-axis scales by two and is labeled h of d for the height of the tip of a javelin in meters. The graph of the function is a continuous curve. From left to right, it starts at the y-intercept zero, five and increases through the point ten, nine, the point twenty, twelve, and the point thirty, thirteen until it reaches a local maximum at forty, fourteen. Then it decreases through the point fifty, thirteen, the point sixty, twelve, the point seventy, nine, and the point eighty, five until it stops at the x-intercept ninety, zero.", "backgroundImage": {"height": 464, "url": "web+graphie:${☣ LOCALPATH}/images/df4caae561ed47c1c09c878bab40dce92754e5a3", "width": 464}, "box": [464, 464], "caption": "", "labels": [], "range": [[0, 10], [0, 10]], "static": false, "title": ""}, "static": false, "type": "image", "version": {"major": 0, "minor": 0}}, "matcher 1": {"alignment": "default", "graded": true, "options": {"labels": ["**Feature**", "**Statement**"], "left": ["$x$-intercept", "Relative maximum or minimum", "Increasing or decreasing interval"], "orderMatters": false, "padding": true, "right": ["Jan threw the javelin to a distance of $90$ meters.", "The highest point the javelin reached was $14$ meters above the ground.", "The javelin began its descent after the $40$-meter mark."]}, "static": false, "type": "matcher", "version": {"major": 0, "minor": 0}}}}}