### Video Transcript

The following graph shows the
function 𝑓 of 𝜃. Assume the function has a period of
two 𝜋. What is the domain of 𝑓 of 𝜃? What is the range of 𝑓 of 𝜃?

We know that all the
characteristics of a periodic function are contained over an interval of this
length. In this question, we are told the
period is equal to two 𝜋. Therefore, we only need to consider
the graph between zero and two 𝜋. The domain of any function is a set
of all possible input values. And we can see from the graph that
the function is well defined at all values of 𝜃. We can therefore conclude that the
domain of 𝑓 of 𝜃 is all real numbers written as the open interval from negative ∞
to ∞.

The range of any function is the
set of all output values. From the graph, we see that the
function oscillates and is continuous between negative seven and three. The maximum value of the graph is
three, and the minimum value is negative seven. We can therefore conclude that the
range of 𝑓 of 𝜃 is the set of values on the closed interval from negative seven to
three. The two answers to this question
are the open interval from negative ∞ to ∞ and the closed interval from negative
seven to three.