# What is the domain and range of h(t)=4/t ?

Jul 12, 2016

The domain is $\left\{x | x \ne 0\right\}$, and the range is $\left\{y | y \ne 0\right\}$.

#### Explanation:

Observing a graph of the function is very helpful in determining the answer here:

We can see that any number will work as an input, except for $0$. This is because $\frac{4}{0}$ is undefined.

Thus, any number except for $0$ is in the domain of the function.

The other thing you may notice is that the function can be an incredibly large value, but while it gets very close to $0$, it never actually reaches that number. ($0$ is the limit of the function as $t \to \infty$ but this is not a defined value).

Thus, any number except for $0$ is in the range of the function.