Here, to 3 significant figures, are 2 functions of

$x = $

$f(x) = $  ,

$g(x) = $  

Before continuing, see if you can get to know these functions better. Use scrolling controls on the x input box to give you access to lots of values quickly. You can type in decimal values.

1. Experiment until you find a value of $x$ where $f(x)$ appears to be the same as $g(x)$.

   How did you narrow the possibilities down to this value of $x$? Is there a general method?

   How close do you think $f(x)$ and $g(x)$ really are at this value? Can you find a value of $x$ where $f(x)$ should be even closer to $g(x)$?

2. Here, again to 3 significant figures, are two more functions of

   $x = $ .

   $f(x) = $   as before, but also:

   $h(x) = $  

   $j(x) = $  

   Experimentally, find values of $x$ and $y$ so that $f(x) = h(x)$ and $f(y) = j(y)$. Compare your findings with others and discuss.

3. What sorts of function are $f, g, h,$ and $j$? Can you find write down expressions for $f, g, h$ and $j$?