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Rencia Lourens RADMASTE Centre Using the CASIO fx-82ZA PLUS for functions in the FET band

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Some remarks A calculator is a tool. Learners should Know where answers come from. Understand mathematics. Teachers should Teach the mathematics. Explain the reasoning behind why the calculator methods work. BUT the calculator can (and should) become a tool to assist.

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CAPS Functions form 35% of the Grade 12 paper 1, 45% in Grade 11 and 30% in Grade 10 (CAPS). The calculator can be used to support the calculations needed to draw and interpret the graphs of the functions.

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Intersection of two graphs Who is NOT sure?

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So how can I as a teacher use this to enhance understanding? Some thoughts The meaning of simultaneous equations. The meaning of a plotted graph.

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Next example

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xf(x)g(x) -5366.25 -4245.25 -3144.25 -263.25 02.25 0-41.25 1-60.25 2-6-0.75 3-4-1.75 40-2.75 56-3.75 f(-2) > g(-2) f(-1) < g(-1) f(3) < g(3) f(4) > g(4)

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xf(x)g(x) -263.25 -1.754.31253 -1.52.75 -1.251.31252.5 02.25

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xf(x)g(x) 3-4-1.75 3.25-3.1875-2 3.5-2.25 3.75-1.1875-2.5 40-2.75

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Turning point of a parabola

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xf(x) -544 -431 -320 -211 4 0 1-4 2-5 3-4 4 54

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So how can I use this as a teacher to enhance understanding? Some thoughts The meaning of symmetry The minimum value The meaning of a plotted graph The shape of a quadratic function Just checking – the turning point is (2; -5)

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New example

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xf(x) -5118 -478 -346 -222 6 0-2 1 26 322 446 578 The turning point should be somewhere between x = 0 and x = 1

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xf(x) 0-2 0.25-2.75 0.5-3 0.75-2.75 1-2

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Next example

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xf(x) -596.5 -470 -347.5 -229 14.5 04 1-2.5 2-5 3-3.5 42 511.5 The turning point should be somewhere between x = 1 and x = 3

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xf(x) 1-2.5 1.25-3.5 1.5-4.25 1.75-4.75 2-5 2.25-5 2.5-4.75 2.75-4.25 3-3.5 The turning point should be somewhere between x = 2 and x = 2.25

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xf(x) 2-5 2.0625-5.0234375 2.125-5.03125 2.1875-5.0234375 2.25-5

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Finding the intercepts with the axes

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xf(x) -556 -442 -330 -220 12 06 12 20 30 42 56 y intercept x intercept Just checking……. Where will the turning point be?

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Next example

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xf(x) -5-43 -4-31 -3-21 -2-13 -7 0-3 1 2 3-3 4-7 5-13 y-intercept Turning point should be here No x-intercept?

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Seems as there are no x- intercepts. Focus on turning point first. Will be between x=1 and x=2. The turning point is below the x-axis. All the graph values are below the x-axis. So no x-intercepts. x 1 1.25-0.8125 1.5-0.75 1.75-0.8125 2

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Next example

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xf(x) -5-119 -4-75 -3-39 -2-11 9 021 125 221 39 4-11 5-38 y-intercept Turning point should be here x-intercept should be here

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Somewhere between x = -2 and x = -1 the one x-intercept should lie and somewhere between x = 3 and x = 4 the other x-intercept should lie. So we are going to look at smaller domains and smaller steps.

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xf(x) -2-11 -1.75-5.25 -1.50 -1.254.75 9 x-intercept

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xf(x) 39 3.254.75 3.50 3.75-5.25 4-11 x-intercept

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Looking at the reciprocal function

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xf(x) -51.333333 -41.2 -31 -20.6666666 0 0-2 1ERROR 221 39 4-11 5--38 y-intercept Asymptote x-intercept

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Finding equations of graphs We now need to move to the STATS mode Let us have a look at the Menu Is everybody sure how to get into STATS mode?

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Example – linear function

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Example – Quadratic function with intercepts given

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Example – Quadratic function with any three points.

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Example – Exponential function* with any two points.

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Example – Quadratic function with the turning point and another point.

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