Solve the Problem $$g ( x ) = - \frac { 1 } { 5 } x ^ { 6 } - 3$$

Solve the problem.
- $$g ( x ) = - \frac { 1 } { 5 } x ^ { 6 } - 3$$ a. Identify the power function of the form $y = x ^ { n }$ that is the parent function to the given graph.
b. In order, outline the transformations that would be required on the graph of $y = x ^ { n }$ to make the Graph of the given function.
c. Match the function with the graph.
i.


ii.


iii.


iv.

A) a. $y = x ^ { 6 }$
b. Expand $y = x ^ { 6 }$ horizontally by a factor of 5 . Reflect across the $x$ - axis. Shift downward 3 units.
c. Graph iv.
B) a. $y = x$
b. Expand $y = x ^ { 6 }$ vertically by a factor of 5 . Reflect across the $x$ - axis. Shift upward 3 units.
c. Graph iv.
C) a. $y = x ^ { 6 }$
b. Shrink $y = x ^ { 6 }$ vertically by a factor of $\frac { 1 } { 5 }$ . Reflect across the $x$ - axis. Shift downward 3 units,
c. Graph $i$ .
D) a. $y = x ^ { 6 }$
b. Shrink $y = x ^ { 6 }$ horizontally by a factor of $\frac { 1 } { 5 }$ . Reflect across the $x -$ axis. Shift downward 3 units.
c. Graph iii.