Question

How do you find the domain and range of `y = 3/x^2`?

Answer 1

Domain: `{x|x !=0}` or `(-oo, 0)uu(0,oo)`

Range: `{y|y>0}` or `(0, oo)`

Explanation:

`y = 3/x^2`

The function is undefined if the denominator is zero, so we set it equal to 0 and solve:

`x^2=0`

`x=+-sqrt0`

`x=0`

So the domain is:

`{x|x !=0}` or `(-oo, 0)uu(0,oo)`

Now as `x` gets close to `-oo` or `oo` the function gets closer to 0 but never actually gets to 0 and as `x` gets very close to 0 the function grows to `oo` so the range is:

`{y|y>0}` or `(0, oo)`

graph{y = 3/x^2 [-10, 10, -5, 5]}