Question

How do you find the domain and range of a function in interval notation?

Answer 1

Hint: The interval notation is the notation that is used to define any particular interval in mathematics . This notation helps us to concisely put forward the range of values in a mathematical expression.

Complete step by step solution:
The interval notation is a type of notation which is used to denote a range of values in a given function for example if the range of a function say $ \sin \theta $ lies between the values $ - 1 $ and $ 1 $ . We will easily write the given range in interval notation as $ [ - 1, - 1] $ . Here we use capital brackets if the value is inclusive of that value as well or use parentheses in case the boundary value is not included in the range. The range of a function is the values a given function produces in the given domain. So sine function above gives the answer in the range of values $ - 1 $ and $ 1 $ .
Domain of a function is the values which a given function accepts for example it could be real numbers excluding the points at which the given function becomes undefined . or has the denominator as zero.
The function for example $ \sin \theta $ has a domain of all real numbers but gives out values only in the range of $ [ - 1,1] $ where both values $ - 1 $ and $ 1 $ are included in the range along with all the numbers. Between them.

Note: The another form we can write the range is in a simple form written like,
 $ 0 \leqslant \theta < 360 $
Which transforms to, $ \theta $ lies in the interval $ [0,360) $ , here $ \theta $ includes 0 but not 360 but values which are less than 360.