12. Without graphing, determine if each polynomial function has line symmetry about the \( y \) -axis, point symmetry about the origin, or neither. Graph the functions to verify your answers. a) \( f ( x ) = - x ^ { 5 } + 7 x ^ { 3 } + 2 x \)
b) \( f ( x ) = x ^ { 4 } + 3 x ^ { 2 } + 1 \)
c) \( f ( x ) = 4 x ^ { 3 } - 3 x ^ { 2 } + 8 x + 1\)
a)
symmetric to origin
b)
symmetric to y - axis
c)
symmetric to ( 0, 1 )
Find the inverse for each of the following functions.
\(f ( x ) = 3 x + 1\)
\(g ( x ) = 1 x ^ { 3 } - 5\)
\(h ( x ) = \frac { 3 } { x + 5 }\)
\(j ( x ) = \sqrt[ 3 ] { x + 1 }\)
The total revenue from the sale of a popular book is approximated by the rational function \( R ( x ) = \frac { 1700 x ^ { 2 } } { x ^ { 2 } + 4 } \) , where \( x \) is the number of years since publication and \( R ( x ) \)
is the total revenue in millions of dollars.
(a) Find the total revenue at the end of the first year.
(b) Find the total revenue at the end of the second year.
