314 RATIONAL FUNCTIONS l 4.1. EXERCISES f: In Exercises 1 - 18. for the given rational function Find the domain of f . Identify any vertica l asymptotes of the graph of y = f ( x). Identify any holes in the graph. Find the horizontal asymptote, if it exists. Find the slant asymptote, if it exists. Graph the function using a graphing utility and describe the behavior near the asymptotes. 1. J( x ) = . /. 6 x- 3x.c- 2. 7x \\/4 f ( x ) = x2 + 5. f ( f (x) = 10. .f (:r) = 3x2 2 13. f ( x ) ? 16. f ( x ) = 5x9- x - 2x 2 = + 5:x 3 3x + x3 1 _ x + = x- x +7 (x+ 6. f ( x ) = x3 x +1 2 - 1 4x +4 .i;2 x 12 3)2 4x 7. x 2 52x x) 1 3. f ( x) = f (x) = 3+ 8. f (x ) = x2 - 4 3 + 2 2 x + x x2 - x - 11. f ( x ) = x 9. f ( x ) = x2 - x - 12 x2 + x - 6 12. f ( x ) = x3 .T _ -1:3 + 4x f ( ) 14. x - x2 9 17. f ( x ) = 1 8 2x2 x2- 9 + -5x4 10 2 15. +1 1 3x3 + x2 - 2 3x 3 f (x ) =--=- ----=-- x - 3x2 + 3x 1 x3 - 4x2 - 4x 5 18. f ( x) = x2 + x + 1 19. The cost C in dollars to remove p% of the invasive species of Ippizuti fish from Sasquatch Pond is given by 0 _< P 100 100 - p ' C(p) = 1770p < (a) Find and interpret C(25) and C(95) . (b) What does the vertical asymptote at x = 100 mean within the context of the problem? (c) What percentage of the Ippizuti fish can you remove for $40000? 20. In Exercise 71 in Section 1.4, the population of Sasquatch in Portage County was modeled by the function P( t) = 150t t + 15) where t = 0 represents the year 1803. Find the horizontal asymptote of the graph of y = P(t) and explain what it means