**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?)**