// Numbas version: exam_results_page_options {"name": "Sketching graphs: sketch 2^x", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"statement": "

This is a non-calculator question.

", "variablesTest": {"maxRuns": 100, "condition": ""}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Student is asked to sketch $f(x)=2^x$, by plotting several points and selecting the correct graph.

"}, "variables": {"y": {"name": "y", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "[2^x[0],\n 2^x[1],\n 2^x[2],\n 2^x[3],\n 2^x[4],\n 2^x[5],\n 2^x[6],\n 2^x[7]]"}, "x": {"name": "x", "templateType": "anything", "group": "Ungrouped variables", "description": "

The y-intercept.

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(i) {answer(x[0],y[0],x[1],y[1],x[2],y[2],x[3],y[3],x[4],y[4],x[5],y[5],x[6],y[6],x[7],y[7],0)}

\n

\n

See Lecture 6.3 for functions and 1.5 and 6.4 for exponentiation.

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{answer(x[0],y[0],x[1],y[1],x[2],y[2],x[3],y[3],x[4],y[4],x[5],y[5],x[6],y[6],x[7],y[7],1)}

", "

{answer(x[0],y[0],x[1],y[1],x[2],y[2],x[3],y[3],x[4],y[4],x[5],y[5],x[6],y[6],x[7],y[7],2)}

", "

{answer(x[0],y[0],x[1],y[1],x[2],y[2],x[3],y[3],x[4],y[4],x[5],y[5],x[6],y[6],x[7],y[7],3)}

", "

{answer(x[0],y[0],x[1],y[1],x[2],y[2],x[3],y[3],x[4],y[4],x[5],y[5],x[6],y[6],x[7],y[7],4)}

"], "matrix": ["2", 0, 0, 0], "customMarkingAlgorithm": "", "minMarks": 0, "displayType": "radiogroup", "customName": ""}], "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "scripts": {}, "variableReplacements": [], "customMarkingAlgorithm": "", "showCorrectAnswer": true, "useCustomName": false, "variableReplacementStrategy": "originalfirst", "customName": "", "marks": 0, "sortAnswers": false, "type": "gapfill", "prompt": "

{dragpoint()}

\n

We want to sketch a graph of the function $f(x) = 2^x$.  We will do this be plotting several points, and then seeing the overall pattern that emerges.

\n

\n

(i) By filling in a table like the one below, drag the points A to H to the correct location.

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
PointABCDEFGH
$x$-3-2-101234
$f(x)$
\n

\n

\n

(Note, to be marked correctly, you only need to move the points to within 0.1 of the exact location.)

\n

\n

\n

\n

(ii) Hence, select the graph of $f(x)=2^x$ from below:

\n

[[8]]

\n

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