Casio 9860 DYNA Investigation and Instructions
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1 Casio 9860 DYNA Investigation and Instructions Instructions This activity is both a self-guided instruction worksheet and a student investigation of Straight Lines, Parabolas, Cubics, Hyperbolas, and Exponentials. 1) Straight line graphs: Investigating the effect of 'A' in Y = AX Select MENU, then DYNA and into the Y1: line enter AX ( then A then ) line. Press EXE. (Fig1) NOTE You must use for X in DYNA, GRAPH and TABLE modes. To set up the axes: Go to View window (SHIFT F3) and select INIT (F1) (Fig2) Press EXIT (Fig1) Fig1 Fig2 Fig3 Screenshots Turning on the axes: Go to SET UP (SHIFT MENU) and arrow up to Axes and turn on with F1 if necessary. Set Grid and Label to Off. Press EXIT. (Fig3) Fig4 To set the values for A: Select VAR (F4). (You will be at screen Fig4 but will have most likely have a different value for A. Select SET (F2) and enter the values according to Fig5, pressing EXE after each entry. Press EXIT. You should be back at a screen like Fig4 Fig5 Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
2 To select the speed: Press SPEED (F3), and set speed to Stop&Go (F1) (Fig6) (you can experiment with this): Press EXIT Fig6 Activating DYNA: Select DYNA (F6) (Fig7) Use EXE to go to the next graph (with the next value of A) (To stop press AC. To restart, EXIT, and press DYNA again) Fig7 QUESTIONS: a) What is the effect when A is positive compared to A being negative? b) What happens to the graph as A moves from 0.5 to 3 (and -0.5 to -3) c) What do we call the co-efficient of X in a straight line graph? 2) Straight line graphs: Investigating the effect of 'B' in Y = 2X + B a) Before entering this into your calculator, what do you think will be the effect of B on the graph? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
3 With DYNA still activated, press AC, EXIT, EXIT and in the Dynamic Function screen enter 2X+B (2 + B ) EXE as shown in Fig8 Arrow up to Y1 and use SEL (F1) to deselect the first graph (Fig9) Fig8 Fig9 Go to View Window (SHIFT F3) and enter the min and max values for X and Y as per Fig10. NOTE: Ignore scale, dot and all other settings Fig10 Press EXIT then press VAR, then SET and enter the values in Fig11 EXIT, and press DYNA (Fig12) Press EXE repeatedly to see the graphs with different values for B b) What effect does B have on the straight line? What is B called? Fig11 Fig12 Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
4 3) Investigating Quadratics (A quadratic equation, when graphed, is called a parabola) Consider: Y = AX 2 Return to the Dynamic function screen. (AC EXIT EXIT) With the cursor over Y2 deselect by pressing F1 (Fig13) Into Y3 enter AX 2 ( A ) and EXE (Fig14) Fig13 Fig14 Go to View Window (SHIFT F3) and enter the min and max values for X and Y as per Fig15. NOTE: Ignore scale, dot and all other settings Fig15 EXIT, select VAR (F4), then select SET (F2) Enter the values as per Fig16 Fig16 EXIT, press SPEED (F3) and select NORMAL (F3) (Fig17) EXIT from there and select DYNA (F6). Fig17 a) How does the number before the X 2 term (the X 2 coefficient) affect the graph? Why does it affect the graph in this way? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
5 4) Investigating Quadratics of the type Y = 2 X 2 + C a) Before we do this, what do you think will be the effect of the C value on the graph? Fig18 Fig19 Stop the DYNA animation (press AC), then EXIT twice. Deselect the previous equation (F1), then type in 2 X 2 + C in Y4 (Fig18) Change the View Window settings according to Fig19, ignoring scale and dot. Fig20 Press EXIT, VAR and SET and enter the dynamic settings as per Fig20 Press EXIT and DYNA. b) What is the effect of C? d) What is the value C called in relation to the graph? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
6 5) Investigating Cubics Return to the Dynamic Function screen: Press AC to turn DYNA off, then EXIT EXIT. Deselect the previous equation and enter AX 3 into Y5 (Fig21) Fig21 a) Before seeing this one, make a small free-hand sketch of your prediction of what any cubic graph will look like? (ie what will be the effect of the cube on the X?) Fig22 Change the View Window according to Fig22 Change the Dynamic Setting as per Fig23 Press EXIT and DYNA. Fig23 b) Describe the effect the value of A has on the graph. c) When A is a negative value what happens to the graph? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
7 Answer the next question before activating DYNA. Consider the cubic Y = 2X 3 + C d) What will be the effect of the C on the graph Y = 2X 3 + C? Return to the Dynamic Function Window, deselect the previous function and enter Y = 2X^3 + C into the (Fig24) Fig24 Leave the View Window settings unchanged but adjust the dynamic setting as per Fig25 Activate DYNA with Y = 2X^3 + C. Were you correct in part c)? Fig25 5) Investigating Exponential Graphs eg Y = N X, Y = N X + 4, Y = N X - 10, etc Go to the Dynamic Function screen, deselect the previous expression and enter Y = N^X + 4 into Y7 (Fig26) Fig26 Change the View Window according to Fig27 Change the Dynamic Setting as per Fig28 Fig27 Press EXIT and DYNA. Choose an appropriate speed setting and press DYNA. a) Why is the graph a straight line when N = 1? Fig28 Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
8 b) What is the equation of the graph when it is a straight line? c) Why does the graph curve when N is greater than 1? Tracing A DYNA Graph: We can t trace graphs in DYNA. But we can in GRAPH mode. With DYNA running in the previous example (Y = N^X + 4) stop it with AC when there is a curved graph on the screen. Then go into GRAPH mode (press MENU then 5). You will see your equations are copied there. Select Y = N X + 4 and DRAW. Now trace with SHIFT F1 (Fig29) e) Use the right-left arrows to scroll to the y intercept. Why does the graph cross the Y axis at 5 (rather than 4)? HINT: Consider the equation. Fig29 f) Trace in the negative X direction. What Y value does the graph get closer and closer to but never touch? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
9 Fig30 6) Investigating Hyperbolas Y = X A Return to DYNA. (MENU then 6) Deselect any selected graphs, then enter A X at Y8 (Fig30) Fig31 Set the View Window to INIT (F1) (Fig31) Set the Dynamic Setting as per Fig32 EXIT and press DYNA (Fig33) a) Why is each graph in 2 parts? Fig32 Fig33 b) Why does the graph move further from the origin as A increases? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
10 Let s see what happens for negative values of N. Change the Dynamic Settings as per Fig34 then EXIT and activate DYNA. c) Why do these graphs lie in the other quadrants? 7) EXTENSION ACTIVITY ONE Let s return to Question 5 (exponential graphs). What happens when the N in Y = N^X + 4 becomes less than 1? Go to the Dynamic Function screen, deselect Y=A X reselect Y = N^X+4 (Fig35) Make sure no other functions are selected. Fig34 Fig35 Fig36 Change the View Window according to Fig36 Fig37 Change the Dynamic Setting as per Fig37 Press DYNA (F6) a) Why does the graph curve upward in the negative X region (on the left) when the N values that are less than 1? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
11 b) Why does the curve get steeper on the left as N changes from 0.9 to 0.1? c) Why is the left curve much steeper when N = 0.1 than the right curve when N = 1.9? d) Experiment with different Dynamic Settings and see what you find! Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
12 8) EXTENSION ACTIVITY TWO We have seen the difference between quadratics and cubics. Let s see what happens for other values of N when Y = X^N Enter Y = X^N into the Dynamic Function screen and de-select other equations (Fig38) Fig38 Change the View Window according to Fig39 Fig39 Change the Dynamic Setting as per Fig40 Fig40 Change the Speed Setting to Slow as per Fig41 Press EXIT then DYNA Fig41 a) Look closely at what is happening. What happens when N is an odd number? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
13 b) What happens when N is an even number? c) What is the difference in the shapes of Y = X 2 and Y = X 10? d) What is the difference in the shapes of Y = X 3 and Y = X 9? Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
14 NOTES: Casio 9860 Graphic Calculator DYNA Investigation and Instructions Richard Andrew
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![Transformations. What are the roles of a, k, d, and c in polynomial functions of the form y a[k(x d)] n c, where n?](/thumbs/95/125766084.jpg "Transformations. What are the roles of a, k, d, and c in polynomial functions of the form y a[k(x d)] n c, where n?")
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