Trident Help

Natural Color Graphing manual · Chapter 9 of 18

Graphing functions

Enter functions, draw them in color, set the window, zoom, trace, solve and sketch.

9.1Enter a function#

Press MENU then 3 to open the Graph app. The list holds Y1, Y2 and so on. Type a function using X,θ,T for X and press EXE: it is stored and the cursor moves to the next line.

  1. MENU 3
  2. Type f(x) EXE
  3. F6 DRAW
  4. F1 TRACE
Graph a function
Example 9.1

Enter two functions

  1. Open Graph and type X² − 4, then X + 2.

    MENU3X,θ,Tx²−4EXEX,θ,T+2EXE
Result of the example "Enter two functions" The display shows: Graph Func :Y= / Y1=X²−4 / Y2=X+2 / Y3= / Y4= / Y5= / SELECT DELETE TYPE TOOL · DRAW.
You should seeY1=X²−4 Y2=X+2
F keyLabelWhat it does
F1SELECTTurns the highlighted function on or off for drawing.
F2DELETEClears the highlighted function.
F3TYPEChooses Y=, r=, Parm or X= for the line.
F4TOOLChooses the color.
F6DRAWDraws the graph.
The Graph function list The display shows: Graph Func :Y= / Y1= / Y2= / Y3= / Y4= / Y5= / SELECT DELETE TYPE TOOL · DRAW.
The Graph function list

9.2Edit, delete, select and color#

Example 9.2

Edit a function

  1. Enter X², go up and right, add 1.

    MENU3X,θ,Tx²EXE▲▶+1EXE
Result of the example "Edit a function" The display shows: Graph Func :Y= / Y1=X²+1 / Y2= / Y3= / Y4= / Y5= / SELECT DELETE TYPE TOOL · DRAW.
You should seeY1=X²+1
Example 9.3

Delete a function

  1. Enter X², go up, press DELETE.

    MENU3X,θ,Tx²EXE▲F2
Result of the example "Delete a function" The display shows: Graph Func :Y= / Y1= / Y2= / Y3= / Y4= / Y5= / SELECT DELETE TYPE TOOL · DRAW.
You should seeY1=
Example 9.4

Turn a function off

  1. Enter X², go up and press SELECT, then DRAW: nothing is drawn.

    MENU3X,θ,Tx²EXE▲F1F6
Result of the example "Turn a function off" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE

Default colors are blue, red and green for Y1, Y2 and Y3. Press F4 (TOOL) and choose Blue, Red, Green, Magnt (magenta) or Black.

Example 9.5

Choose a color

  1. Enter X, go up, TOOL, F2 (Red), then DRAW.

    MENU3X,θ,TEXE▲F4F2F6
Result of the example "Choose a color" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE
The color menu The display shows: Graph Func :Y= / Y1= / Y2= / Y3= / Y4= / Y5= / Blue Red Green Magnt Black ▷.
The color menu

9.3Draw a graph#

Press F6 (DRAW). The graph appears with the bar TRACE, ZOOM, V-WIN, SKETCH, G-SOLV, G⇔T. The default window shows X from -6.3 to 6.3 and Y from -3.1 to 3.1. The arrow keys scroll the window. EXIT or F6 (G⇔T) returns to the function list.

Example 9.6

Draw a parabola

  1. Enter X² − 4 and press DRAW.

    MENU3X,θ,Tx²−4EXEF6
    After step 1: Enter X² − 4 and press DRAW. The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
Result of the example "Draw a parabola" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE ZOOM V-WIN SKETCH G-SOLV
Example 9.7

Draw a hyperbola

  1. Enter 1/X and draw.

    MENU31/X,θ,TEXEF6
Result of the example "Draw a hyperbola" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE
Example 9.8

Back to the list

  1. Draw, then EXIT.

    MENU3X,θ,TEXEF6EXIT
Result of the example "Back to the list" The display shows: Graph Func :Y= / Y1=X / Y2= / Y3= / Y4= / Y5= / SELECT DELETE TYPE TOOL · DRAW.
You should seeGraph Func

9.4Set the View Window#

Press SHIFTV-WINF3 (V-WIN) for the View Window: Xmin, Xmax, scale, dot, Ymin and so on. Type a value and press EXE to go to the next line. The bar gives three presets.

F keyPresetWindow
F1INITIALX from -6.3 to 6.3, Y from -3.1 to 3.1.
F2TRIGX from -3π to 3π (or -540 to 540 in degrees), Y from -1.6 to 1.6.
F3STANDRDX and Y from -10 to 10.
The View Window The display shows: View Window / Xmin:-6.3 / max:6.3 / scale:1 / dot:0.0333333333 / Ymin:-3.1 / INITIAL TRIG STANDRD · · ·.
The View Window
Example 9.9

Standard window

  1. Enter X, open V-WIN, choose STANDRD, EXIT and draw.

    MENU3X,θ,TEXESHIFTV-WINF3F3EXITF6
Result of the example "Standard window" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE
Example 9.10

Type your own window

  1. V-WIN, Xmin -5, Xmax 5, EXIT.

    MENU3X,θ,TEXESHIFTV-WINF3(−)5EXE5EXE
Result of the example "Type your own window" The display shows: View Window / Xmin:-5 / max:5 / scale:1 / dot:0.0264550265 / Ymin:-3.1 / INITIAL TRIG STANDRD · · ·.
You should seeXmin:-5
Example 9.11

An impossible window

  1. Set Xmin to 9, which is above Xmax, then draw.

    MENU3SHIFTV-WINF39EXEEXITF6
Result of the example "An impossible window" The display shows: Range ERROR / Press:[EXIT].
You should seeRange ERROR

9.5Zoom in and out#

From the graph screen press F2 (ZOOM). Page 1: BOX, FACT, IN, OUT, AUTO. Page 2 (F6): ORIG, SQR, INTG, PRE.

LabelWhat it does
BOXDrag a box with the arrows: EXE at one corner, then at the opposite corner.
FACTSets the zoom factors for IN and OUT.
IN, OUTZoom around the centre (move the pointer with the arrows to zoom elsewhere), then EXE.
AUTOFits the Y range to the curve.
ORIGBack to the window before zooming.
SQREqual units on both axes.
INTGOne unit per screen dot.
PRESwap with the previous window.
The ZOOM bar, page 1 The display shows: BOX FACT IN OUT AUTO ▷.
The ZOOM bar, page 1
Example 9.12

Zoom in

  1. Draw X, ZOOM, IN, EXE.

    MENU3X,θ,TEXEF6F2F3EXE
Result of the example "Zoom in" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE
Example 9.13

Zoom out

  1. Draw X, ZOOM, OUT, EXE.

    MENU3X,θ,TEXEF6F2F4EXE
Result of the example "Zoom out" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE
Example 9.14

Auto zoom

  1. Draw X², ZOOM, AUTO.

    MENU3X,θ,Tx²EXEF6F2F5
Result of the example "Auto zoom" The display shows: TRACE ZOOM V-WIN SKETCH G-SOLV G⇔T.
You should seeTRACE

9.6Trace along a graph#

Press F1 (TRACE) or SHIFTTRACEF1. A cursor starts at the centre of the window. The top line names the function and the second line gives X and Y. ▶ and ◀ move one dot; type a number and press EXE to jump to that X; ▲ and ▼ switch between graphs. EXIT stops tracing.

Example 9.15

Start tracing

  1. Draw X² − 4 and press TRACE.

    MENU3X,θ,Tx²−4EXEF6F1
    After step 1: Draw X² − 4 and press TRACE. The display shows: Y1=X²−4 / X=0 Y=-4.
Result of the example "Start tracing" The display shows: Y1=X²−4 / X=0 Y=-4.
You should seeY1=X²−4 X=0 Y=-4
Example 9.16

Jump to X = 3

  1. Type 3 and EXE while tracing.

    MENU3X,θ,Tx²−4EXEF6F13EXE
Result of the example "Jump to X = 3" The display shows: Y1=X²−4 / X=3 Y=5.
You should seeX=3 Y=5
Example 9.17

Step with the arrow keys

  1. Press right.

    MENU3X,θ,Tx²−4EXEF6F1▶
Result of the example "Step with the arrow keys" The display shows: Y1=X²−4 / X=0.0333333333 Y=-3.998888889.
You should seeX=0.0333333333 Y=-3.998888889
Example 9.18

Switch between graphs

  1. Two graphs; press down while tracing.

    MENU3X,θ,Tx²EXEX,θ,T+2EXEF6F1▼
Result of the example "Switch between graphs" The display shows: Y2=X+2 / X=0 Y=2.
You should seeY2=X+2

9.7Find roots, maximums and intersections (G-SOLV)#

From the graph screen press F5 (G-SOLV). Page 1: ROOT, MAX, MIN, Y-ICPT, ISECT. Page 2 (F6): Y-CAL, X-CAL, ∫dx. After a result, press ▶ or ◀ to see the next one.

LabelFinds
ROOTWhere the graph crosses the X axis.
MAX, MINThe highest or lowest point in the window.
Y-ICPTWhere the graph crosses the Y axis.
ISECTWhere two graphs cross.
Y-CALY for an X you type.
X-CALEvery X for a Y you type.
∫dxThe area under the graph between two X values, shaded.
Example 9.19

Roots of x² − 4

  1. Draw it and choose ROOT.

    MENU3X,θ,Tx²−4EXEF6F5F1
    After step 1: Draw it and choose ROOT. The display shows: Y1=X²−4 / ROOT / X=-2 Y=0.

  2. Press right for the next root.

    ▶
Result of the example "Roots of x² − 4" The display shows: Y1=X²−4 / ROOT / X=2 Y=0.
You should seeX=2 Y=0
Example 9.20

Minimum

  1. MIN of X² − 4.

    MENU3X,θ,Tx²−4EXEF6F5F3
Result of the example "Minimum" The display shows: Y1=X²−4 / MIN / X=0 Y=-4.
You should seeX=0 Y=-4
Example 9.21

Y-intercept

  1. Y-ICPT of X² − 4.

    MENU3X,θ,Tx²−4EXEF6F5F4
Result of the example "Y-intercept" The display shows: Y1=X²−4 / Y-ICEPT / X=0 Y=-4.
You should seeY-ICEPT X=0 Y=-4
Example 9.22

Where two graphs cross

  1. Draw X² and X + 2, choose ISECT.

    MENU3X,θ,Tx²EXEX,θ,T+2EXEF6F5F5

  2. Right for the second crossing.

    ▶
Result of the example "Where two graphs cross" The display shows: Y1=X² / INTSECT / X=2 Y=4.
You should seeX=2 Y=4
Example 9.23

Y for a given X

  1. Y-CAL with X = 3.

    MENU3X,θ,Tx²−4EXEF6F5F6F13EXE
Result of the example "Y for a given X" The display shows: Y1=X²−4 / Y-CAL / X=3 Y=5.
You should seeX=3 Y=5
Example 9.24

Area under a curve

∫01x2 dx\int_0^1 x^2\,dx

  1. ∫dx from 0 to 1 for X².

    MENU3X,θ,Tx²EXEF6F5F6F30EXE1EXE
Result of the example "Area under a curve" The display shows: Y1=X² / ∫dx / ∫dx=0.3333333333.
You should see∫dx=0.3333333333
Example 9.25

No root exists

  1. Draw X² + 1 and look for roots.

    MENU3X,θ,Tx²+1EXEF6F5F1
Result of the example "No root exists" The display shows: Not Found / Press:[EXIT].
You should seeNot Found

9.8Draw a tangent or normal line#

Press F4 (SKETCH): Cls clears sketches, Tang draws a tangent, Norm a normal. Type the X value and press EXE twice. The slope dy/dx is shown.

Example 9.26

Tangent at x = 1

  1. Draw X², SKETCH, Tang, 1, EXE, EXE.

    MENU3X,θ,Tx²EXEF6F4F21EXEEXE
Result of the example "Tangent at x = 1" The display shows: Y1=X² / X=1 Y=1 / dy/dx=2.
You should seedy/dx=2
The SKETCH bar The display shows: Cls Tang Norm · · ·.
The SKETCH bar

fx-CG50 is a trademark of Casio Computer Co., Ltd.. Trident Calculator is an independent product by South View Studios and is not affiliated with, sponsored by or endorsed by Casio. The name is used only to describe the kind of calculator this model resembles; Trident's names, keys, display, fonts and software are its own clean-room design.