This document provides 40 examples of tutorials that construct function tables and graphs for cube root functions of the form y=cuberoot(ax+b)+c. Each tutorial varies the values of a, b, and c to illustrate different forms of cube root functions.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
A hands-on activity for explore a variety of math topics, including:
* Circumference and Diameter
* Linear functions and slope
* Ratios
* Data gathering and scatterplot
For more math resources, go to www.media4math.com.
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SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
A hands-on activity for explore a variety of math topics, including:
* Circumference and Diameter
* Linear functions and slope
* Ratios
* Data gathering and scatterplot
For more math resources, go to www.media4math.com.
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2. Overview
This set of tutorials provides 40 examples of cube
root functions in tabular and graph form.
3. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 01. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) with these characteristics: a = 1, b = 0.
4. Tutorial--Square Root Functions in Tabular and Graph Form: Example 02. In this
tutorial, construct a function table and graph for a square root function of the form y
= sqrt(ax +b) with these characteristics: a > 1, b = 0.
5. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 03. In
this tutorial, construct a function table and graph for a cube root function of
the form y = cuberoot(ax +b) with these characteristics: a < -1, b = 0.
6. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 04. In
this tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) with these characteristics: 0 < a < 1, b = 0.
7. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 05. In
this tutorial, construct a function table and graph for a cube root function of
the form y = cuberoot(ax +b) with these characteristics: -1 < a < 0, b = 0.
8. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 06. In
this tutorial, construct a function table and graph for a cube root function of
the form y = cuberoot(ax +b) with these characteristics: a = 1, b = 1.
9. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 07. In
this tutorial, construct a function table and graph for a cube root function of
the form y = cuberoot(ax +b) with these characteristics: a > 1, b = 1.
10. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 08. In
this tutorial, construct a function table and graph for a cube root function of
the form y = cuberoot(ax +b) with these characteristics: a < -1, b = 1.
11. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 09. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) with these characteristics: 0 < a < 1, b = 1.
12. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 10. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) with these characteristics: -1 < a < 0, b = 1.
13. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 11. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: a = 1, b = 0, c = 1.
14. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 12. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a > 1, b = 0, c = 1.
15. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 13. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a < -1, b = 0, c = 1.
16. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 14. In this
tutorial, construct a function table and graph for a cube root function of the form y
= cuberoot(ax +b) + c with these characteristics: 0 < a < 1, b = 0, c = 1.
17. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 15. In this
tutorial, construct a function table and graph for a cube root function of the form y
= cuberoot(ax +b) + c with these characteristics: -1 < a < 0, b = 0, c = 1.
18. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 16. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a = 1, b = 1, c = 1.
19. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 17. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a > 1, b = 1, c = 1.
20. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 18. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: a < -1, b = 1, c = 1.
21. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 19. In this
tutorial, construct a function table and graph for a cube root function of the form y
= cuberoot(ax +b) + c with these characteristics: 0 < a < 1, b = 1, c = 1.
22. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 20. In this
tutorial, construct a function table and graph for a cube root function of the form y
= cuberoot(ax +b) + c with these characteristics: -1 < a < 0, b = 1, c = 1.
23. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 21. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: a = 1, b = 0, c = -1.
24. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 22. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a > 1, b = 0, c = -1.
25. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 23. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: a < -1, b = 0, c = -1.
26. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 24. In this
tutorial, construct a function table and graph for a cube root function of the form y
= cuberoot(ax +b) + c with these characteristics: 0 < a < 1, b = 0, c = -1.
27. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 25. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: -1 < a < 0, b = 0, c = -1.
28. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 26. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a = 1, b = 1, c = -1.
29. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 27. In this
tutorial, construct a function table and graph for a cube root function of the
form y = cuberoot(ax +b) + c with these characteristics: a > 1, b = 1, c = -1.
30. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 28. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: a < -1, b = 1, c = -1.
31. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 29. In this
tutorial, construct a function table and graph for a cube root function of the form y
= cuberoot(ax +b) + c with these characteristics: 0 < a < 1, b = 1, c = -1.
32. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 30. In this
tutorial, construct a function table and graph for a cube root function of the form
y = cuberoot(ax +b) + c with these characteristics: -1 < a < 0, b = 1, c = -1.
33. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 31. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: a = 1, b = 0, c = -1, d
= -1.
34. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 32. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: a > 1, b = 0, c = -1, d
= -1.
35. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 33. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: a < -1, b = 0, c = -1,
d = -1.
36. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 34. In this tutorial,
construct a function table and graph for a cube root function of base 10 of the form y= d •
sqrt(ax +b) + c with these characteristics: 0 < a < 1, b = 0, c = -1, d = -1.
37. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 35. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: -1 < a < 0, b = 0, c
= -1, d = -1.
38. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 36. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: a = 1, b = 1, c = -1,
d = -1.
39. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 37. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: a > 1, b = 1, c = -1,
d = -1.
40. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 38. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: a < -1, b = 1, c = -1,
d = -1.
41. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 39. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: 0 < a < 1, b = 1, c =
-1, d = -1.
42. Tutorial--Cube Root Functions in Tabular and Graph Form: Example 40. In this
tutorial, construct a function table and graph for a cube root function of base 10
of the form y= d • sqrt(ax +b) + c with these characteristics: -1 < a < 0, b = 1, c
= -1, d = -1.