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Classic CAS manual · Chapter 14 of 16

Graphing

Plot functions, trace, change the window, zoom, find zeros, extremes and intersections, and use parametric and polar graphs.

14.1The graphs page#

Press doc to open the Graphs page. It first shows the function list: f1(x) to f7(x). Type a rule in a line, press ▼ to go to the next line, and press enter or tab to draw. Press tab or esc on the graph to return to the list. Letters you have stored as variables can be used in the rules.

The function list. The display shows: Graphs: Function tab: graph / f1(x)= / f2(x)= / f3(x)= / f4(x)= / f5(x)= / f6(x)= / f7(x)=.
The function list.
Example 14.1

Plot a parabola

  1. Press doc, then type x² − 4.

    docx^2▶−4
    After step 1: Press doc, then type x² − 4. The display shows: Graphs: Function tab: graph / f1(x)=x^2−4 / f2(x)= / f3(x)= / f4(x)= / f5(x)= / f6(x)= / f7(x)=.

  2. Press enter to plot.

    enter
Result of the example "Plot a parabola" The display shows: f1(x)=x^2-4 / x=0 y=-4.
You should seef1(x)=x^2-4 x=0 y=-4
Example 14.2

Use a stored variable

  1. Store k := 3, open graphs, type k·x, plot, then move right five times.

    k:=3enterdock×xenter▶▶▶▶▶
Result of the example "Use a stored variable" The display shows: f1(x)=3·x / x=1 y=3.
You should seex=1 y=3
Example 14.3

Two functions

  1. Type x, press down, type −x, plot, then press down to move the trace to f2.

    docx▼(−)xenter▼
Result of the example "Two functions" The display shows: f2(x)=-x / x=0 y=0.
You should seef2(x)=-x
Example 14.4

Back to the list

  1. Plot x, then press tab.

    docxentertab
Result of the example "Back to the list" The display shows: Graphs: Function tab: graph / f1(x)=x / f2(x)= / f3(x)= / f4(x)= / f5(x)= / f6(x)= / f7(x)=.
You should seef1(x)=x Graphs: Function

14.2Trace along a graph#

On a plotted graph, a trace point sits at x = 0. Press ▶ and ◀ to move it; the coordinates are shown at the bottom. With several functions, ▲ and ▼ switch between them. Type a number to jump to that x value.

Example 14.5

Move the trace

  1. Plot x² − 4, then press right five times.

    docx^2▶−4enter▶▶▶▶▶
Result of the example "Move the trace" The display shows: f1(x)=x^2-4 / x=1 y=-3.
You should seex=1 y=-3
Example 14.6

Jump to a value of x

  1. Plot x², type 3, and press enter.

    docx^2▶enter3enter
Result of the example "Jump to a value of x" The display shows: f1(x)=x^2 / x=3 y=9.
You should seex=3 y=9
Example 14.7

Value from the Analyze menu

  1. Plot x²−4, then menu, 4, 5 (Value), and type 3.

    docx^2▶−4entermenu453enter
Result of the example "Value from the Analyze menu" The display shows: f1(x)=x^2-4 / x=3 y=5.
You should seex=3 y=5

14.3Change the window and zoom#

The Graph menu (menu on the Graphs page) holds: 1 Window Settings, 2 Zoom, 3 Trace, 4 Analyze Graph, 5 Graph Type, 6 Edit Functions, 7 Toggle Function On/Off, 8 Delete All Functions. The standard window runs from −10 to 10 in x and about −6.67 to 6.67 in y.

The Graph menu. The display shows: Graph Menu / 1: Window Settings / 2: Zoom / 3: Trace / 4: Analyze Graph / 5: Graph Type / 6: Edit Functions / 7: Toggle Function On/Off.
The Graph menu.
Window Settings: XMin, XMax, XScale, YMin, YMax, YScale. The display shows: Window Settings / XMin=-10 / XMax=10 / XScale=1 / YMin=-6.67 / YMax=6.67 / YScale=1.
Window Settings: XMin, XMax, XScale, YMin, YMax, YScale.
Example 14.8

Set the window

  1. Plot x, open menu 1, and type −5, enter.

    docxentermenu1(−)5enter
    After step 1: Plot x, open menu 1, and type −5, enter. The display shows: Window Settings / XMin=-5 / XMax=10 / XScale=1 / YMin=-6.67 / YMax=6.67 / YScale=1.

  2. Type 5, enter, then press enter four times to finish.

    5enterenterenterenterenter
Result of the example "Set the window" The display shows: f1(x)=x / x=0 y=0.
You should seef1(x)=x
Zoom choiceWindow it sets
1 Standardx from −10 to 10, y from −6.67 to 6.67
2 Trigx from −2π to 2π, y from −4 to 4, x scale π/2
3 FitKeeps x, adjusts y to show every function
4 InHalves the window around the trace
5 OutDoubles the window
6 SquareMakes the y range match the screen shape
7 Decimalx from −15.9 to 15.9, y from −10.6 to 10.6
Example 14.9

Zoom to a trig window

  1. Plot sin(x), press menu, 2, 2.

    docsin(x)entermenu22
    After step 1: Plot sin(x), press menu, 2, 2. The display shows: f1(x)=sin(x) / x=0 y=0.
Result of the example "Zoom to a trig window" The display shows: f1(x)=sin(x) / x=0 y=0.
You should seef1(x)=sin(x)
Example 14.10

Zoom in

  1. Plot x, press menu, 2, 4 to halve the window.

    docxentermenu24

  2. Open Window Settings to see the new limits.

    menu1
Result of the example "Zoom in" The display shows: Window Settings / XMin=-5 / XMax=5 / XScale=1 / YMin=-3.335 / YMax=3.335 / YScale=1.
You should seeXMin=-5 XMax=5

14.4Find zeros, minimums, maximums and intersections#

Open the Analyze Graph menu (menu, 4). Zero, Minimum and Maximum search near the trace point and move the trace to the answer. Intersection looks for where two plotted functions meet. If nothing is found, the screen says "No … found".

The Analyze Graph menu. The display shows: Analyze Graph / 1: Zero / 2: Minimum / 3: Maximum / 4: Intersection / 5: Value (x=?).
The Analyze Graph menu.
Example 14.11

Zero to the right

  1. Plot x²−4, move right once, then Analyze, Zero.

    docx^2▶−4enter▶menu41
Result of the example "Zero to the right" The display shows: f1(x)=x^2-4 / zero x=2 y=0.
You should seezero x=2 y=0
Example 14.12

Zero found from x = 0

  1. Without moving, Zero picks the nearer left zero.

    docx^2▶−4entermenu41
Result of the example "Zero found from x = 0" The display shows: f1(x)=x^2-4 / zero x=-2 y=0.
You should seex=-2 y=0
Example 14.13

Minimum

  1. Plot x²−2x, Analyze, Minimum.

    docx^2▶−2xentermenu42
Result of the example "Minimum" The display shows: f1(x)=x^2-2·x / minimum x=1 y=-1.
You should seeminimum x=1 y=-1
Example 14.14

Maximum

  1. Plot 4−x², Analyze, Maximum.

    doc4−x^2▶entermenu43
Result of the example "Maximum" The display shows: f1(x)=-x^2+4 / maximum x=0 y=4.
You should seemaximum x=0 y=4
Example 14.15

Intersection

  1. Type x, down, 2−x, plot, Analyze, Intersection.

    docx▼2−xentermenu44
Result of the example "Intersection" The display shows: f1(x)=x / intersection x=1 y=1.
You should seeintersection x=1 y=1
Example 14.16

Nothing found

  1. Plot x², Analyze, Maximum.

    docx^2▶entermenu43
Result of the example "Nothing found" The display shows: f1(x)=x^2 / No maximum found x=0 y=0.
You should seeNo maximum found

14.5Parametric and polar graphs#

Choose Graph Type (menu, 5) to switch between Function, Parametric and Polar. Parametric lines come in pairs (x1(t) then y1(t)); polar graphs use r1(θ). Typing θ uses θ.

x=cos⁡t,y=sin⁡tx=\cos t,\quad y=\sin t
A parametric circle.
Example 14.17

A parametric circle

  1. Open graphs, menu, 5, 2 (Parametric).

    docmenu52

  2. Type cos(t), down, sin(t), enter.

    cos(t)▼sin(t)enter
Result of the example "A parametric circle" The display shows: x1(t)=cos(t) / t=0 x=1 y=0.
You should seex1(t)=cos(t)
Example 14.18

Trace a parametric curve

  1. Move the trace twice to the right.

    docmenu52cos(t)▼sin(t)enter▶▶
Result of the example "Trace a parametric curve" The display shows: x1(t)=cos(t) / t=0.261799 x=0.965926 y=0.258819.
You should seet=0.261799
r=2sin⁡(3θ)r=2\sin(3\theta)
A three-petal polar rose.
Example 14.19

A polar rose

  1. Choose Polar (menu, 5, 3), type 2 sin(3θ), plot, and trace.

    docmenu532sin(3θ)enter▶▶
Result of the example "A polar rose" The display shows: r1(θ)=2·sin(3·θ) / θ=0.261799 x=1.36603 y=0.366025.
You should seer1(θ)=2·sin(3·θ) θ=0.261799

14.6Turn functions off and clear them#

Edit Functions (menu, 6) returns to the list. Toggle Function On/Off (menu, 7) hides the selected function without erasing it. Delete All Functions (menu, 8) empties the list. If every function is off, the screen says "All functions are off: menu › Toggle Function On/Off"; with no functions at all it says "No functions: tab to enter f1(x)".

Example 14.20

Every function turned off

  1. Plot x, then menu, 7 to turn it off.

    docxentermenu7
Result of the example "Every function turned off" The display shows: All functions are off: menu › Toggle Function On/Off.
You should seeAll functions are off: menu › Toggle Function On/Off

TI-Nspire CX CAS is a trademark of Texas Instruments Incorporated. Trident Calculator is an independent product by South View Studios and is not affiliated with, sponsored by or endorsed by Texas Instruments. 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.