Construct the graph of the function
`f(x)=-|(x^(2)-9)/(x+3)-x+(2)/(x-1)|` and comment upon the following
(a) `(-oo,0)`
(b) `uarr ` in `(1, 5/3)` and `darr` in `(-oo,1)uu(5/3,oo)-{-3}`
(c) `x=5/3`
(a) Range of the function,
(b) Intervals of monotonocity,
(c) Point(s) where f is continuous but not differentiable,
(d) Point(s) where f fails to be continuous and nature of discontinuity.
(e) Gradient of the curve where f crosses the axis of y.

Answer

(a)`(-oo, 0] ` (b) `uarr` in `(1, 5/3)` and `darr` in `(-oo, 1) uu (5/3, oo) -{-3}` (c) `x=5/3`
(d) removable discont.at `x=-3` (missing point ) and non removable discont. at `x=1` (infinite type) (e) `-2`