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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) f(-2) > g(-2) f(-1) < g(-1) f(3) < g(3) f(4) > g(4)

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xf(x)g(x)

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xf(x)g(x)

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Turning point of a parabola

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xf(x)

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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) The turning point should be somewhere between x = 0 and x = 1

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xf(x)

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Next example

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xf(x) The turning point should be somewhere between x = 1 and x = 3

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xf(x) The turning point should be somewhere between x = 2 and x = 2.25

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xf(x)

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Finding the intercepts with the axes

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xf(x) y intercept x intercept Just checking……. Where will the turning point be?

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Next example

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xf(x) 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

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Next example

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xf(x) 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) x-intercept

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xf(x) x-intercept

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Looking at the reciprocal function

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xf(x) ERROR 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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