6. Consider a parabola \( P \) that is congruent to \( y = x ^ { 2 } \) , opens upward, and has vertex \( ( 2 , - 4 ) \) . Now find the equation of a new parabola that results if \( P \) is
a) stretched vertically by a factor of \( 5 \)
b) compressed by a factor of \( \frac { 1 } { 2 } \)
c) translated \( 2 \) units to the left
d) translated \( 3 \) units up
e) reflected in the \( x \) -axis and translated \( 2 \) units to the right and \( 4 \) units down
a) \(y = 5(x - 2)^2 - 4\)
b) \(y = 0.5(x - 2)^2 - 4\)
c) \(y = x^2 - 4\)
d) \(y = (x - 2)^2 - 1\)
e) \(y = - (x - 4)^2 - 8\)
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.
