Quickly sketch each of the following functions.

1. $f\left(x\right) = \left(x − 1\right)^{2}\left(x − 3\right)^{3}\left(x − 5\right)^{2}$

   Answer (a):

   

2. $g\left(x\right) = −\left(x − 1\right)^{2}\left(x − 3\right)^{3}\left(x − 5\right)^{2}$

   Answer (b):

   

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

   Hint (c):

   $g\left(x\right) = \left(?\right) · f\left(x\right)$