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

Aug 23, 2017

Domain: {x| x≠0}
Range: $\left\{y | y > 0\right\}$

#### 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 $\left\{y | y > 0\right\}$.

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