Question

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

Answer 1

Domain: `{x| x≠0}`
Range: `{y| y>0}`

Explanation:

The domain is the input of the function. In this case, the domain has a restriction. The denominator can never be equal to 0. Since we have `x^2` in the denominator, we must set that equal to 0 to find what values of x are not allowed.

`x^2≠0 ->`

`sqrt(x^2)≠sqrt(0)`

`x≠0`

Our domain is `{x|x≠0}`.

Next is to find the range. In this case, note that the range cannot be equal to 0 since we have a variable in the denominator. To find the range, you can plug in numbers to find out what the range is. There is a simpler way to find it. If you input smaller numbers for x, your output for y will be larger. A larger input for x will result in a smaller input for y. As seen in the following graph, the range approaches but never touches or crosses the x-axis. The range also goes to infinity, so the the range is `{y|y>0}`.

graph{2/(x^2) [-10, 10, -5, 5]}