Question

Determine the region(s) of the Cartesian plane for which

a) y > 1/(x^2)

b) y less than or equal to x^2 +4 and y greater than or equal to 1/(x^2 +4)

Answer 1

In general
if y > f(x) you would have the region <b>above</b> the graph of f(x)
and if y < f(x) you would have the region <b>below</b> the graph of f(x).

for y > 1/(x^2)
graph y = 1/(x^2), which would lie totally above the x-axis, with the x-axis a horizontal asymptote and the y-axis a vertical asymptote.
So the regions would be the two parts above the graph, one above the curve in quadrant I and the other above the curve in quadrant II.

For the second you want the intersection of the regions (AND is used)
the top curve is a parabola with vertex (0,4), so you want the region below that
The second curve is a variation of the "witch of Agnesi" curve
((Broken Link Removed)
and you want the region above that.
So shade in the intersection of the two regions.
I wish there was an easy way to illustrate by graphing.