Projects - Cengage Learning

C-54 Appendix C
y
1
-4
-3
-2
-1
1 2 3 4
x
-1
Figure D
A graph of
f(x) b 1, 0 x 1 , f(x) 0 for integer x, and f(x 2) f(x).
1, 1 x 0
The next two problems guide you through the construction of a sawtooth wave
and a triangular wave.
1. Sawtooth wave: Consider the function g defined by g(x) x for 0 x 1.
(a) Graph y g(x).
(b) Extend g to be an odd function for 1 x 1. Graph this odd version
of g.
(c) Extend the odd version of g to be a periodic function with period 2.
Graph this odd and periodic version of g.
(d) Finally extend the odd and periodic version of g to have domain all
real numbers. Graph this odd and periodic version of g with domain all
real numbers. This graph is called a sawtooth wave.
2. Triangular wave: Consider the function h defined by h(x) x for 0 x 1.
(a)
(b)
Graph y h(x).
Extend h to be an even function for 1 x 1. Graph this even
version of h.
(c) Extend the even version of h to be a periodic function with period 2.
Notice the domain is all real numbers. Graph this even and periodic
version of h with domain all real numbers. This graph is called a
triangular wave.