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

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

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.

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.

Intersection of two graphs Who is NOT sure?

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.

Next example

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)

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

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

Turning point of a parabola

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

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)

New example

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

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

Next example

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

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

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

Finding the intercepts with the axes

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?

Next example

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?

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

Next example

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

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.

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

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

Looking at the reciprocal function

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

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?

Example – linear function

Example – Quadratic function with intercepts given

Example – Quadratic function with any three points.

Example – Exponential function* with any two points.

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

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