TI 84 Plus CE: Building Piecewise Functions by Points
Introduction
The program PWISEBLD generates a parametric piecewise function in the form:
x(t) = t
y(t) = p(t) (piecewise function)
The program allows the user to draw lines from 2 to 5 points.
Point 1: (A, B)
Point 2: (C, D)
Point 3: (E, F)
Point 4: (G, H)
Point 5: (I, J)
p(t) =
(Kt + B - KA)(A ≤ t ≤ C) +
(LT + D - LC)(C < t ≤ E) +
(Mt + F - ME)(E < t ≤ G) +
(Nt + H - NG)(G < t ≤ I)
where the comparisons evaluate to either 0 (false) or 1 (true)
The program was typed on the TI-84 Plus CE but it should work with any of the TI-80 (?), TI-81 (?), TI-82, TI-83, and TI-84 families.
TI-84 Plus Program PWISEBLD
"2020-02-24 EWS"
Param
FnOff
ClrHome
Disp "PIECEWISE BY POINTS", "PARAMETRIC MODE"
Lbl 0
Input "POINTS (2,3,4,5)?", O
iPart(O) → O
If O<2 o="" or="">5
Then
Disp "2,3,4 OR 5 ONLY"
Goto 0
End
"DATA"
"T" → X1T
Disp "(A,B)?"
Prompt A,B
A → Tmin
Disp "(C,D)?"
Prompt C,D
C → Tmax
(D - B) / (C - A) → K
"(KT + B - KA)(A ≤ T and T ≤ C)" → Str0
If O ≥ 3
Then
Disp "(E,F)?"
Prompt E,F
E → Tmax
(F - D) / (E - C) → L
Str0 + "+(LT+D-LC)(C
End
If O ≥ 4
Then
Disp "(G,H)?"
Prompt G,H
G → Tmax
(H - F) / (G - E) → M
Stro + "+(MT+F-ME)(E
End
If O = 5
Then
Disp "(I,J)?"
Prompt I,J
I → Tmax
(J - H) / (I - G) → N
Str0 + "+(NT+H-NG)(G
End
Str0 → Y1T
"SET GRAPH"
ZoomFit
Download the TI-84 Plus CE version:
https://drive.google.com/open?id=1195hC6LBkR6uHCmCTjWAybSb07YwEPIa
You can use the parametric function Y1T(t) for analysis.
Examples
Example 1:
Three Points: (3, 4), (5, 6), (8, 1)
Example 2:
Four Points: (0, 0), (3, 4), (5, 6), (8, 1)
Example 3:
Five Points: (0, 0), (1, 1), (3, 6), (6, 10), (9, 12)
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
Introduction
The program PWISEBLD generates a parametric piecewise function in the form:
x(t) = t
y(t) = p(t) (piecewise function)
The program allows the user to draw lines from 2 to 5 points.
Point 1: (A, B)
Point 2: (C, D)
Point 3: (E, F)
Point 4: (G, H)
Point 5: (I, J)
p(t) =
(Kt + B - KA)(A ≤ t ≤ C) +
(LT + D - LC)(C < t ≤ E) +
(Mt + F - ME)(E < t ≤ G) +
(Nt + H - NG)(G < t ≤ I)
where the comparisons evaluate to either 0 (false) or 1 (true)
The program was typed on the TI-84 Plus CE but it should work with any of the TI-80 (?), TI-81 (?), TI-82, TI-83, and TI-84 families.
TI-84 Plus Program PWISEBLD
"2020-02-24 EWS"
Param
FnOff
ClrHome
Disp "PIECEWISE BY POINTS", "PARAMETRIC MODE"
Lbl 0
Input "POINTS (2,3,4,5)?", O
iPart(O) → O
If O<2 o="" or="">5
Then
Disp "2,3,4 OR 5 ONLY"
Goto 0
End
"DATA"
"T" → X1T
Disp "(A,B)?"
Prompt A,B
A → Tmin
Disp "(C,D)?"
Prompt C,D
C → Tmax
(D - B) / (C - A) → K
"(KT + B - KA)(A ≤ T and T ≤ C)" → Str0
If O ≥ 3
Then
Disp "(E,F)?"
Prompt E,F
E → Tmax
(F - D) / (E - C) → L
Str0 + "+(LT+D-LC)(C
End
If O ≥ 4
Then
Disp "(G,H)?"
Prompt G,H
G → Tmax
(H - F) / (G - E) → M
Stro + "+(MT+F-ME)(E
End
If O = 5
Then
Disp "(I,J)?"
Prompt I,J
I → Tmax
(J - H) / (I - G) → N
Str0 + "+(NT+H-NG)(G
End
Str0 → Y1T
"SET GRAPH"
ZoomFit
Download the TI-84 Plus CE version:
https://drive.google.com/open?id=1195hC6LBkR6uHCmCTjWAybSb07YwEPIa
You can use the parametric function Y1T(t) for analysis.
Examples
Example 1:
Three Points: (3, 4), (5, 6), (8, 1)
Example 2:
Four Points: (0, 0), (3, 4), (5, 6), (8, 1)
Example 3:
Five Points: (0, 0), (1, 1), (3, 6), (6, 10), (9, 12)
Eddie
All original content copyright, © 2011-2020. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.