This section is about finding the domain and range of a function. First, we'll need to discuss interval notation, which is the method we'll use to answer domain and range questions.
Interval Notation
Let's first talk about interval notation. This is the notation that we use to answer with a range of numbers. This notation is similar to how we learned to shade number lines in a previous math class.
"Shaded/solid/closed" points or brackets [], mean we should include that number.
"Unshaded/open" points or parentheses () mean we don't include that number.
Once we choose the marker on the endpoints of our interval, we shade in between. This is how we graphed an interval on a number line, and it very closely relates to how we write the interval in interval notation.
When writing intervals, the smallest number in the interval always goes on the left, and the largest number in the interval on the right, with a comma in between. Then we use parentheses or brackets, as above, to indicate the value is not included or included, as appropriate.
When we have multiple intervals that a value could be in, we use a union operator.
Video
Watch this video for some examples using interval notation.
Domain
The domain of a function is the set of all the values that are permitted as input values for the function.
When determining the domain, we check for:
- numbers that produce division by zero
- numbers that produce a negative inside an even root
Video
Watch this video for some examples of finding domain algebraically.
Now, we'll define range and look at some graphs to determine both the domain and the range.
Range
The range of a function is the set of outputs given from the function.
Video
Watch this video for some examples of finding domain and range from looking at a graph. Sometimes, we can use our intuition to find range, but most often we will need to use the graph to determine the range.