This document outlines 54 tutorials that provide examples of constructing tables and graphs for exponential functions of various bases (2, 10, e) and characteristics of the coefficients a and b. Each tutorial works through an example of an exponential function of the form y = a*b^x, varying the values of a and b to illustrate different patterns in the table and graph.
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.
MODULE 5 QuizQuestion1. Find the domain of the function. E.docxmoirarandell
MODULE 5 Quiz
Question
1.
Find the domain of the function. Express your answer in interval notation.
a.
b.
c.
d.
2.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
3.
Graph f(x) = |x – 1|.
a.
b.
c.
d.
4.
Determine whether the function is even, odd, or neither. f(x) = x5 + 4
a. Even
b. Odd
c. Neither
5.
Find the value of f(3) if f(x) = 4x2 + x.
a. 38
b. 39
c. 40
d. 41
6.
Use the graph of the function to estimate: (a) f(–6), (b) f(1), (c) All x such that f(x) = 3
a. (a) 4 (b) 3 (c) –5, 1
b. (a) 5 (b) 4 (c) –3, 1
c. (a) 1 (b) 2 (c) –5, 2
d. (a) 7 (b) 5 (c) –5, 6
7.
The graph of the function g is formed by applying the indicated sequence of transformations to the given function f. Find an equation for the function g. The graph of is horizontally stretched by a factor of 0.1, reflected in the y axis, and shifted four units to the left.
a.
b.
c.
d.
8.
Evaluate f(–1).
a. –1
b. 8
c. 0
d. –2
9.
Determine whether the function is even, odd, or neither. f(x) = x3 – 10x
a. Even
b. Odd
c. Neither
10.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
11.
Determine whether the equation defines a function with independent variable x. If it does, find the domain. If it does not, find a value of x to which there corresponds more than one value of y. x|y| = x + 5
a. A function with domain all real numbers
b. A function with domain all real numbers except 0
c. Not a function: when x = 0, y = ±5
d. Not a function: when x = 1, y = ±6
12.
Graph y = (x – 2)2 + 1
a.
b.
c.
d.
13.
Find the y-intercept(s).
a. –2
b. 1, –3
c. –3
d. None
14.
Determine whether the correspondence defines a function. Let F be the set of all faculty teaching Chemistry 101 at a university, and let S be the set of all students taking that course. Students from set S correspond to their Chemistry 101 instructors.
a. A function
b. Not a function
15.
Determine whether the function is even, odd, or neither. f(x) = –4x2 + 5x + 3
a. Even
b. Odd
c. Neither
16.
Indicate whether the table defines a function.
a. Function
b. Not a function
17.
Use the graph of the function to estimate: (a) f(1), (b) f(–5),and (c) All x such that f(x) = 3
a. (a) –3 (b) –9 (c) 7
b. (a) –3 (b) –9 (c) –1
c. (a) 5 (b) –1 (c) 7
d. (a) 5 (b) –1 (c) –1
18.
Find the intervals over which f is increasing.
a. (–∞, –2], [1, ∞)
b. (–3, ∞)
c. (–∞, –3], [1, ∞)
d. None
19.
Evaluate f(4).
a. 4
b. 10
c. 5
d. –2
20.
Indicate whether the graph is the graph of a function.
a. Function
b. Not a function
21.
Sketch the graph of the function f(x) = –2x + 3.
a.
b.
22.
Find the intervals over which f is decreasing.
a. (–∞, –2), [1, ∞)
b. (–∞, –2], [1, ∞)
c. (–∞, –3), [1, ∞)
d. (–∞, –3], [1, ∞)
23.
Indicate whether the table defines a function.
a. Function
b. Not a function
24.
Indicate whether the graph is the graph of a function.
a. ...
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2. Overview
This set of tutorials provides 54 examples of
exponential functions in tabular and graph form.
3. Tutorial--Exponential Functions in Tabular and Graph Form: Example 01. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = 1, b = 1.
4. Tutorial--Exponential Functions in Tabular and Graph Form: Example 02. In this
tutorial, construct a function table and graph for an exponential function of base
2 of the form y = a*2^(bx) with these characteristics: a > 1, b = 1.
5. Tutorial--Exponential Functions in Tabular and Graph Form: Example 03. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = 1, b > 1.
6. Tutorial--Exponential Functions in Tabular and Graph Form: Example 04. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a > 1, b > 1.
7. Tutorial--Exponential Functions in Tabular and Graph Form: Example 05. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = -1, b = -1.
8. Tutorial--Exponential Functions in Tabular and Graph Form: Example 06. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a < -1, b = -1.
9. Tutorial--Exponential Functions in Tabular and Graph Form: Example 07. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = -1, b < -1.
10. Tutorial--Exponential Functions in Tabular and Graph Form: Example 08. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a < -1, b < -1.
11. Tutorial--Exponential Functions in Tabular and Graph Form: Example 09. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: -1 < a < 0, b = 1.
12. Tutorial--Exponential Functions in Tabular and Graph Form: Example 10. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = 1, -1 < b < 0.
13. Tutorial--Exponential Functions in Tabular and Graph Form: Example 11. In this
tutorial, construct a function table and graph for an exponential function of base
2 of the form y = a*2^(bx) with these characteristics: -1 < a < 0, -1 < b < 0.
14. Tutorial--Exponential Functions in Tabular and Graph Form: Example 12. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: -1 < a < 0, b = -1.
15. Tutorial--Exponential Functions in Tabular and Graph Form: Example 13. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = -1, -1 < b < 0.
16. Tutorial--Exponential Functions in Tabular and Graph Form: Example 14. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: 0 < a < 1, b = 1.
17. Tutorial--Exponential Functions in Tabular and Graph Form: Example 15. In
this tutorial, construct a function table and graph for an exponential function
of base 2 of the form y = a*2^(bx) with these characteristics: a = 1, 0 < b < 1.
18. Tutorial--Exponential Functions in Tabular and Graph Form: Example 16. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: 0 < a < 1, 0 < b < 1.
19. Tutorial--Exponential Functions in Tabular and Graph Form: Example 17. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: 0 < a < 1, b = -1.
20. Tutorial--Exponential Functions in Tabular and Graph Form: Example 18. In
this tutorial, construct a function table and graph for an exponential function of
base 2 of the form y = a*2^(bx) with these characteristics: a = -1, 0 < b < 1.
21. Tutorial--Exponential Functions in Tabular and Graph Form: Example 19. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = 1, b = 1.
22. Tutorial--Exponential Functions in Tabular and Graph Form: Example 20. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a > 1, b = 1.
23. Tutorial--Exponential Functions in Tabular and Graph Form: Example 21. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = 1, b > 1.
24. Tutorial--Exponential Functions in Tabular and Graph Form: Example 22. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a > 1, b > 1.
25. Tutorial--Exponential Functions in Tabular and Graph Form: Example 23. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = -1, b = -1.
26. Tutorial--Exponential Functions in Tabular and Graph Form: Example 24. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a < -1, b = -1.
27. Tutorial--Exponential Functions in Tabular and Graph Form: Example 25. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a = -1, b < -1.
28. Tutorial--Exponential Functions in Tabular and Graph Form: Example 26. In
this tutorial, construct a function table and graph for an exponential function
of base 10 of the form y = a*10^(bx) with these characteristics: a < -1, b < -1.
29. Tutorial--Exponential Functions in Tabular and Graph Form: Example 27. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: -1 < a < 0, b = 1.
30. Tutorial--Exponential Functions in Tabular and Graph Form: Example 28. In this
tutorial, construct a function table and graph for an exponential function of base
10 of the form y = a*10^(bx) with these characteristics: a = 1, -1 < b < 0.
31. Tutorial--Quadratic Functions in Tabular and Graph Form: Example 29. In
this tutorial, construct a function table and graph for a quadratic function in
standard form with these characteristics: a < -1, b < -1, c = -1.
32. Tutorial--Exponential Functions in Tabular and Graph Form: Example 30. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: -1 < a < 0, b = -1.
33. Tutorial--Exponential Functions in Tabular and Graph Form: Example 31. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: a = -1, -1 < b < 0.
34. Tutorial--Exponential Functions in Tabular and Graph Form: Example 32. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: 0 < a < 1, b = 1.
35. Tutorial--Exponential Functions in Tabular and Graph Form: Example 33. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: a = 1, 0 < b < 1.
36. Tutorial--Exponential Functions in Tabular and Graph Form: Example 34. In this
tutorial, construct a function table and graph for an exponential function of base
10 of the form y = a*10^(bx) with these characteristics: 0 < a < 1, 0 < b < 1.
37. Tutorial--Exponential Functions in Tabular and Graph Form: Example 35. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: 0 < a < 1, b = -1.
38. Tutorial--Exponential Functions in Tabular and Graph Form: Example 36. In
this tutorial, construct a function table and graph for an exponential function of
base 10 of the form y = a*10^(bx) with these characteristics: a = -1, 0 < b < 1.
39. Tutorial--Exponential Functions in Tabular and Graph Form: Example 37. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: a = 1, b = 1.
40. Tutorial--Exponential Functions in Tabular and Graph Form: Example 38. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a > 1, b = 1.
41. Tutorial--Exponential Functions in Tabular and Graph Form: Example 39. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = 1, b > 1.
42. Tutorial--Exponential Functions in Tabular and Graph Form: Example 40. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a > 1, b > 1.
43. Tutorial--Exponential Functions in Tabular and Graph Form: Example 41. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = -1, b = -1.
44. Tutorial--Exponential Functions in Tabular and Graph Form: Example 42. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a < -1, b = -1.
45. Tutorial--Exponential Functions in Tabular and Graph Form: Example 43. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = -1, b < -1.
46. Tutorial--Exponential Functions in Tabular and Graph Form: Example 44. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a < -1, b < -1.
47. Tutorial--Exponential Functions in Tabular and Graph Form: Example 45. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: -1 < a < 0, b = 1.
48. Tutorial--Exponential Functions in Tabular and Graph Form: Example 46. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: a = 1, -1 < b < 0.
49. Tutorial--Exponential Functions in Tabular and Graph Form: Example 47. In this
tutorial, construct a function table and graph for an exponential function of base
e of the form y = a*e^(bx) with these characteristics: -1 < a < 0, -1 < b < 0.
50. Tutorial--Exponential Functions in Tabular and Graph Form: Example 48. In this
tutorial, construct a function table and graph for an exponential function of base
e of the form y = a*e^(bx) with these characteristics: -1 < a < 0, b = -1.
51. Tutorial--Exponential Functions in Tabular and Graph Form: Example 49. In this
tutorial, construct a function table and graph for an exponential function of base
e of the form y = a*e^(bx) with these characteristics: a = -1, -1 < b < 0.
52. Tutorial--Exponential Functions in Tabular and Graph Form: Example 50. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: 0 < a < 1, b = 1.
53. Tutorial--Exponential Functions in Tabular and Graph Form: Example 51. In
this tutorial, construct a function table and graph for an exponential function
of base e of the form y = a*e^(bx) with these characteristics: a = 1, 0 < b < 1.
54. Tutorial--Exponential Functions in Tabular and Graph Form: Example 52. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: 0 < a < 1, 0 < b < 1.
55. Tutorial--Exponential Functions in Tabular and Graph Form: Example 53. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: 0 < a < 1, b = -1.
56. Tutorial--Exponential Functions in Tabular and Graph Form: Example 54. In
this tutorial, construct a function table and graph for an exponential function of
base e of the form y = a*e^(bx) with these characteristics: a = -1, 0 < b < 1.