Question

How do you graph `y =1/x^2`?

Answer 1

The graph of this function looks like a bell centred around the y axis.

Explanation:

First you must ensure that the denominator is different from zero so you set:
`x!=0`

The y axis becomes a vertical asymptote of your function; basically the graph of your function will be a curve that gets as near as possible to the y axis without ever crossing it.

When `x` gets near zero (but not zero!) the function becomes very big positively (try with `x=0.001` you get `y=1/0.001^2=1,000,000) while when`x`becomes very large (positively or negatively) the function tends to become very small (try with`x=100`you get:`y=1/100^2=0.0001#).
So your graph will look like:
graph{1/x^2 [-10, 10, -5, 5]}

This function is particularly interesting when describing the phenomenon of Resonance in physics!