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

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["y0", "number"], ["x1", "number"], ["y1", "number"], ["x2", "number"], ["y2", "number"], ["x3", "number"], ["y3", "number"], ["x4", "number"], ["y4", "number"], ["x5", "number"], ["y5", "number"], ["x6", "number"], ["y6", "number"], ["x7", "number"], ["y7", "number"], ["n", "number"]]}, "dragpoint": {"type": "html", "definition": "// set up the board\nvar xmin = -5;\nvar xmax = 5;\nvar ymin = -5;\nvar ymax = 20;\n\nvar div = Numbas.extensions.jsxgraph.makeBoard('500px','500px',\n {boundingBox: [xmin,ymax,xmax,ymin],\n grid:true,labels:true});\nvar board = div.board;\n\n// create the x-axis and y-axis\nvar xaxis = board.create('axis',[[0,0],[1,0]]);\n\n// create the y-axis\nvar yaxis = board.create('axis',[[0,0],[0,1]], );\n\n\n\nvar a = board.create('point',[-3,0],{size:3});\nvar b = board.create('point',[-2,0],{size:3});\nvar c = board.create('point',[-1,0],{size:3});\nvar d = board.create('point',[0,0],{size:3});\nvar e = board.create('point',[1,0],{size:3});\nvar f= 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Numbas.math.niceNumber(e.Y());\n Numbas.exam.currentQuestion.parts[0].gaps[4].display.studentAnswer([[x0,y0]]);\n});\nf.on('drag',function(){\n var x0 = Numbas.math.niceNumber(f.X());\n var y0 = Numbas.math.niceNumber(f.Y());\n Numbas.exam.currentQuestion.parts[0].gaps[5].display.studentAnswer([[x0,y0]]);\n});\ng.on('drag',function(){\n var x0 = Numbas.math.niceNumber(g.X());\n var y0 = Numbas.math.niceNumber(g.Y());\n Numbas.exam.currentQuestion.parts[0].gaps[6].display.studentAnswer([[x0,y0]]);\n});\nh.on('drag',function(){\n var x0 = Numbas.math.niceNumber(h.X());\n var y0 = Numbas.math.niceNumber(h.Y());\n Numbas.exam.currentQuestion.parts[0].gaps[7].display.studentAnswer([[x0,y0]]);\n});\n\nreturn div;\n\n\n", "language": "javascript", "parameters": []}}, "variables": {"y": {"templateType": "anything", "name": "y", "description": "", "group": "Ungrouped variables", "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": {"templateType": "anything", "name": "x", "description": "

The y-intercept.

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

", "

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{dragpoint()}

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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.

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(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
 Point A B C D E F G H \$x\$ -3 -2 -1 0 1 2 3 4 \$f(x)\$
\n

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

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

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[[8]]

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This is a non-calculator question.

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