Quickly sketch each of the following functions.

1. $f(x) = (x - 1)^2(x - 3)^3(x - 5)^2$ 

   Answer (a):

   

2. $g(x) = -(x - 1)^2(x - 3)^3(x - 5)^2$ 

   Hint (b):

   How is this different from the function in part (a)?
   What transformation is created by a negative sign?

3. Express $g(x)$ in terms of $f(x)$. 

   Hint (c):

   Look at your graphs from parts (a) and (b).
   What do they tell you about the relationship between the two functions?

   Answer (c):

   $g(x) = -f(x)$