For each equation below, make tables that include x-values from $−2$ to $2$ and draw each graph.

1. $y = \left(x − 1\right)^{2}\left(x + 1\right)$

   Answer (a):

   $\left. \begin{array} { | c | c | } \hline x & { y } \\ \hline - 2 & { - 9 } \\ { - 1 } & { 0 } \\ { 0 } & { 1 } \\ { 1 } & { 0 } \\ { 2 } & { 3 } \end{array} \right|$

   

2. $y = \left(x − 1\right)^{2}\left(x + 1\right)^{2}$

   Answer (b):

   $\left. \begin{array} { | c | c | } \hline x & { y } \\ \hline - 2 & { 9 } \\ { - 1 } & { 0 } \\ { 0 } & { 1 } \\ { 1 } & { 0 } \\ { 2 } & { 9 } \end{array} \right|$

   

3. $y = x^{3} − 4x$

   Hint (c):

   Use the same method as in parts (a) and (b).

4. What are the parent functions for these equations?

   Hint (d):

   What is the highest-valued exponent?

   Example (d):

   The parent function is $y = x^{3}$.
   $y = \left(x − 1\right)^{2}\left(x + 1\right)\\y = \left(x^{2} − 2x + 1\right)\left(x + 1\right)\\y = x^{3} − x^{2} − x + 1$