# How do you find the domain and range of h(t) = 1/(t^2)?

May 17, 2017

See below.

#### Explanation:

The domain of a function relates to its $x$ value, or in this case, $t$. The range is the function, or $h \left(t\right)$.

$\frac{1}{0}$ is undefined, which happens when $t = 0$, so the domain does not include zero.

Since the denominator is squared, the range of the function will never be negative.

As $t$ approaches infinity, $h \left(t\right)$ approaches $0$.
As $t$ approaches zero, $h \left(t\right)$ also approaches $\infty$.

Thus, the domain is $\left(\infty , 0\right) \cup \left(0 , \infty\right)$, and the range is $\left(0 , \infty\right)$.