1. Graph a function with following properties. X - - BE lim f (x) =0, lim f (x)=co, lim f (x) =1, f(0) =5 E - + * X -0 x -4 lim f ( x) = -20, lim f (x)=co, lim f(x) =2 a) State the intervals of continuity for f (x) b) State the vertical and horizontal asymptotes of f (x) 2. Determine the intervals on which f (x ) is continuous, show all your work and justify your conclusions: 2x+1 if xnFind the following limits, show all your work to justify your conclusions: 3. lim 2x -11x 2 - x 2 *-5" xz - 5x 4. lim tan-' 1 + x 5. lim - x- 11 10x - 3 at x -8 6. lim * - -0/16x2 +7 COS ( XX) 7. lim8. Find all the vertical and horizontal asymptotes of the function f ( x) = 5x3 - 5x- -60x , justify x- - 4x2 each asymptote with limit explanation