The graph of g(x)
= sin(10x)
is getting squished (or damped) between the graphs of
y = x
and y = -x
!!Don't believe me? Then check
it out! Let's graph f(x)
= x*sin(10x),
y = x
and y =
-x
all on the same graph...
(y=x and y= -x are
the thicker lines.)
We see that our sine graph
is, indeed, bounded between them! Pretty cool, huh?
In the function
this x is called
the damping factor.
Let's try something more complicated.
What would the graph of
f(x) = (log
x)*cos(15x) look
like?
Well, g(x)
= cos(15x)
looks like:
(graphing window: x on [-.235, 7], y on [-1.5, 1.5])
Our damping factor is
log
x. So, g(x)
= cos(15x)
is going to get bounded by
y = log
x and
y = -log
x . (Note
that g(x)=cos(15x) is also going to get restricted to the
domain of y=log(x) which is x>0.)
Let's see what it will look
like!
(graphing window: x on [-.235, 7], y on [-1.5, 1.5])
It sure looks like it's bounded
by those logs... Let's graph them to be sure!
Yep!
(Looks like the messy end of a fish, doesn't it?)
