Question

x^2 - 4
What are the:
Intervals on which the graph is above the x axis
Intervals on which the graph is below the x axis
Intervals on which the function is increasing
Intervals on which the function is increasing
Im not sure how to write these intervals.. so then i can do the other examples..

Answer 1

let y = x^2 - 4 and sketch it

here is a picture, using that sketch you should be able to answer all questions

http://www.wolframalpha.com/input/?i=plot+y+%3D+x%5E2+-+4

e.g.
"Intervals on which the graph is below the x axis "
----> -2 < x < 2

Answer 2

I will do some of these.
graph is above x axis when x^2-4>0 or
x^2>4 or
-2>x>2

when below
x^2-4<0
x^2<4
-2<x<2

when increasing:
(x+e)^2-4>x^2-4 where e is a very small number Now expanding
x^2+2xe+e^2-4-x^2+4>0
2xe+e^2>0
because e is always a positive number, this is true when x is positive. Answer
increasing when x>0