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GRAPHING CALCULATORS

(1) 2-Dimensional Graphs: Generate 2-dimensional graphs of 3 equations. Include copies of these graphs in your portfolio.

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(2) Evaluate Graphs: Generate graphs to show how evaluation features (derivative, integral, etc.) can be used to explain a math or science concept.

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Sinx graph-calculating the area.

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(3) 3-Dimensional Graphs: Graph 3-dimensional graphs of 2 equations of your choice. To graph in three dimensions; type a function of x and y, starting with z=. Rotate the graph and include printouts of each graph in two distinctly different positions.

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(4) Inequalities: You can graph inequalities simply by plotting them using the greater than or lesser than signs. The colored zones represent the solution to the inequality. Below are graphs of three inequalities. Determine the equations to these graphs and confirm your answers using the graphing calculator. Equation:

!

sin(x) " y > 0

Equation:

!

y2

+ x2

<16 Equation:

!

y " 4(x " 3)2

> 0

(a)

(b)

(c)

!

sin(x) " y > 0

!

y2

+ x2

<16

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!

y " 4(x " 3)2

> 0

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(d) Include printouts of the following inequalities in your portfolio:

cos10! <tan(rsin 2r)

x2

22 + y

2<2

2

cos6! < sinr

(5) Solving Simultaneous Equations The solution(s) to simultaneous equations can be determined by identifying the points where the equations for two graphs intersect. For example, to solve two simultaneous equations (e.g. y=cos x and y=sin x2), simply set them equal to each other (cos x = sin x2), examine the plot, and click at the points where they intersect to obtain the values for x and y.

xcos x2

sin=

Circled Areas

Represent Solutions Find the solution(s) to the following equations using the graphing calculator. Give the x and y coordinates of the solutions (if any), and include graphs of the solutions in your portfolios. The graphs should zoom in on the points of intersection.

!

cos10" < tan(rsin2r)

!

x2

22

+ y2

< 22

!

cos6" < sinr

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(1) y = x2 y = sin2(x)

(2) y = x2+1 y = x

(3) y = cos(x) y = x / 3

(4) y =x

3sin x+ 5 y = x3

(5) y = x

1

2 y = x 2

(1)

(2)

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(3)

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(4)

(5)

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(6) Educational Applications: Write three questions, tasks, or objectives that illustrate how to use a graphing program to improve math or science instruction. Include graphs and specify the objective or standard addressed, class and grade level. Visualizing Graphs:

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