Question

Find the asymptote, interval of monotonicity, critical points, the local extreme points, intervals of concavity and inflection point of the following functions. Sketch the graph.
a)f(x)=|x2 +x-2|

Answer 1

assuming you just need to confirm your answers, I'll say
none
|x+.5|>1.5
monotone over any interval not including the x-values -2,-.5,1
up: x<-2 and x>1
down: -2<x<1
no inflection

http://www.wolframalpha.com/input/?i=|x^2+%2Bx-2|

Answer 2

given the student's use of strange exponent notation it might be

|x^2 + 1/x^2 |

http://www.wolframalpha.com/input/?i=|x^2+%2Bx^-2|