What is the domain and range of the function f(t)=7.2t models the average distance f(t) in kilometers that BOB rides his bike over time ,t, in hours?

Oct 8, 2015

Domain and range are $\mathbb{R}$ but they can be limited (see explanation)

Explanation:

Generally, since for every real $t$ the value can be calculated, the domain is $\mathbb{R}$, and the range is the same. It is a linear function and its range and domain are $\mathbb{R}$.

However if it is to be a model of a physical process the domain and range could be limited.

The domain of the function as a model of a process would be ${\mathbb{R}}_{+}$ (i. e. only positive real numbers) because it is not possible for the time to go backwards.

The same limitations could be applied to the range. This can be explained in 2 ways:

1) If $t$ is a positive number, then $7.2 \cdot t$ is also positive.
2) You could also give the same reason as in case of the domain. The distance travelled cannot be negative.