parabola (quadratic) square root semicircle (top, bottom, both) or ellipse or use template greatest integer (step) graphed with int() 10.

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Kelly Fletcher
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1 Calculator Art Algebra Two DUE Monday MAY 19, 2014 The purpose of this project is for you to program your nspire calculator to draw a picture that incorporates many of the basic graphs that we have studied in class as well as your knowledge of transformations (vertical shifts, vertical stretches and shrinks, horizontal shifts). Here is a list of the Basic Graphs that you can/must use: 1. y = mx + b slanted or oblique line ( m 0) 2. y = c constant (horizontal line). y = x absolute value 4. y 2 = x parabola (quadratic) 5. y = x cubic c 6. y = x hyperbola (inverse variation hyperbola) or use template 7. y = x square root y =± r x semicircle (top, bottom, both) or ellipse or use template 9. y = [ x] greatest integer (step) graphed with int() 10. y = x cube root 11. y = 2 x exponential ( easy chair ) 12. y = tan x tangent 1. y = sin x or y = cos x sinusoid 14. y = x identity 15. y = kx direct variation 16. x=c vertical line Requirements: 1. every picture must contain at least one sinusoid (#1) 2. 6 different Basic Graphs including #1 makes you eligible for a C. 8 different Basic Graphs including #1 makes you eligible for a B different Basic Graphs including #1 makes you eligible for an A different Basic Graphs makes you eligible for bonus points 6. You must use some sort of transformation on at least 90% of your functions 7. You must use restricted domains on at least 80% of your functions (see the explanation on page of this document for restricted domains) You can t use restricted domain with the template graphs. 8. You must have a minimum of 10 functions graphed 9. Your picture must be recognizable 10. Bonus points can also be earned for extra creative drawings as perceived by the teacher 11. You can use the draw feature to help your picture, but a drawn circle won t count as a circle equation #8 for example. 12. Be sure your graphs are different. Graphing 6 different parabolas is ONE graph. For example, graphing a parabola, a line, an absolute value, a cube root, an exponential, and a constant, would be 6 DIFFERENT graphs, making you eligible for a C. 1

2 What You Will Turn In When Finished 2 In addition to your Nspire file! The axes must be hidden in the file you turn in. 1. Either a hand drawn sketch of your picture drawn before your calculator picture was constructed, OR a print out of a picture that you wanted to have your calculator draw. 2. A sentence or two explaining what your picture is.. A list of all the functions (equations) that you used in your drawing classified by number (1 to 16 from the list above). You do not need to list the restricted domain. PLEASE ASK IF YOU DO NOT UNDERSTAND THIS LIST!!! It would be a silly way to lose points. For example if you used two linear graphs then you would list 1) for linear and then the equations, then you didn t use any constants then 2) none, and you used two absolute values ) then your absolute value equations. Your list would look like this: 1) y = 2x + y = - x + 1 2) none (in other words, you didn t use a constant) ) y = x 4 y = x+ 1 2 Etc PLEASE PLEASE PLEASE do not just list your equations. It would be difficult to ascertain which one is which. 4. A paragraph discussing the following: (please label your answers: a, b, c, d, e, f.) a) what you liked about this project b) what you disliked about this project c) what you learned while doing this project d) what problems that you encountered while doing this project e) any other comments you would like to share f) approximate amount of time you needed to complete this project outside of class Helpful Hints 1. Name your Nspire file as follows: First Initial, Last Name, space, calcart For example, my file name would be: ebrowne calcart 2. Send your file to the classroom computer early and often! (Doc, file, send) There is no excuse for lost files or nspires that turn off and lose your work, or your roommate/friend/dorm mate/classmate/sibling borrowing it.. It doesn t matter what Window you use so pick an easy one to work with. You may want to only work in the first quadrant. That is up to you. But pick a Window that allows you to draw your picture easily and clearly. I found 0 (x) and 20 (y) worked pretty well. 4. SAVE SAVE SAVE SAVE SAVE every time you smile, SAVE 5. If you have the computer software that came with your nspire, load it and do this project on the computer it s a lot bigger and easier to work with.

6. You will need to use either the such that symbol or the piece wise template to restrict the

templates button c) Choose the piecewise template The entry line for the graph will be on the top

3 6. You will need to use either the such that symbol or the piece wise template to restrict the domain of your function. This template is above the multiplication (times) sign. The such that symbol is in ctrl =. Here are the steps for both: a) Open a graph page IN A DOCUMENT NOT THE SCRATCHPAD b) Press the templates button c) Choose the piecewise template The entry line for the graph will be on the top of the page on our updated calculators. (like step a) d) Change the default number from to 1. e) Write your function in the first box and the restricted domain in the second. Example:

f) You may want to hide the equations so they don t clutter up your screen.

hide plot labels g) Here it is without the equation but you can still see the equation by pressing

h) To use such that follow the same steps but type your equation first, then use the such that symbol

If you use the example here you need to make your screen bigger to see it Such that This graph is

4 f) You may want to hide the equations so they don t clutter up your screen. 4 be sure you are on a graph screen, choose menu, then settings then check the box to automatically hide plot labels g) Here it is without the equation but you can still see the equation by pressing tab or ctrl g. h) To use such that follow the same steps but type your equation first, then use the such that symbol and type your domain restriction. If you use the example here you need to make your screen bigger to see it Such that This graph is using -1 to 5 as the restricted domain, 7. When you are finished, or you just want to see what it looks like without the axes, you can hide the axes. From the Graph page, select menu, View, Hide Axes 8. You can also hide the Entry Line -- See choice 7 in the figure above. Or use ctrl g.

5 9. Continue to build your picture with more and more functions defined in pieces. 10. You can also change the attributes of your lines by right clicking (crtl menu) on the line you want to change, and choosing attributes. You can make them thicker, dotted or dashed, and you can also change the color. Ctrl menu, color to change the color. 11. To graph a vertical line, follow these steps: a. Menu-action-text. Click anywhere in the white area and type your equation. Remember that if you want a restricted range, type that in as well. For example: x = 1 < y < will graph a vertical line at x= between a range of -1 and. b. Press enter, press escape (to put away the text tool), then grab your equation and drag it to the axis, the line should appear. Keep in mind that I did not type in the bracket that appears in the picture. I typed it exactly as written above, with the such that symbol. The nspire creates the bracket when you press enter. See tips below if you are having difficulties with this. c. 12. Remember to save your work so that if the calculator should crash, you will have most of the work saved. I also suggest that you save it with more than one name, that is, have a backup file. You can also send it during any class, so that it is saved in the class folder. Be sure you are logged in and press ~, file, send. Or go to my docs, highlight the file name and press menu, send. There is NO EXCUSE for lost files. 1. Another way to graph a conic or a vertical line, press menu, graph entry/edit, equation. This is useful if you just need the whole shape/line or you just want to have a quick way of seeing how it looks. You CANNOT restrict the domain doing it this way. 14. HAVE FUN!! Tips: When graphing an x=, if you are having trouble: 1. press esc to clear any open tools. 2. If the graph is on the page and you are trying to restrict the domain, then point to it, crtl-menu and choose edit relation. (point to the graph, not the equation). In the entry line that opens at the top of the page, type in your restricted domain after your equation, (using such that and y) and be sure that x(x)= has not appeared instead of x=. If it has, just edit it so it just reads x=. Don t forget to press enter to graph it. 4. When you are translating (moving) an x= graph, remember that the h and k are reversed. The k moves it same sign horizontally and the h moves it opposite sign vertically. The x= graph works on sins, semicircles, parabolas etc. 5. Don t forget to drag the equation to the axis to graph it if the graph is NOT on the page. NOTE: Tom Reardon created this project with input from several other teachers and he thanks them for their assistance and willingness to share: Jane Barnard from Missouri Corey Boby from Arkansas Betty Mayberry from Tennessee Retha Gipson, Susan Creekmore, and Heather Riddle from Arkansas Ron Lancaster from Ontario, Canada Robert Rowe from Missouri Travis Bower also contributed to this lesson Edited from the original Tom Reardon file for Algebra Two Pomfret School I appreciate that Tom Reardon puts all his lessons on line so we can all share. 5

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