Be the Professor: Blog #4

Hello class! I’m Professor Jenna and today’s lesson is about domain and range. Domain and range are very important when interpreting a graph or understanding the x and y values of a function. You will need this information to analyze graphs and whatnot. 

So, what is domain? Domain is the set of input values that go into a graph or function. These points define the function. And what is range? Range is the set of all the output values of function.

For example, the surface area of a cube is the total outside area of the cube. It can be found by using the formula: A = 6x². Let us assume that you are asked to construct a cube that has a side length of at least 3 inches. In order to identify the domain, you must first identify the independent variable. Since the independent variable is the length of a side, then the domain has to describe numbers that could represent lengths of sides for this problem – the problem says the length has to be at least 3 inches, so the domain is all numbers greater than or equal to 3.

In order to identify the range, you must first identify the domain. The range is the y-value that corresponds with the chosen x-value in a function. So, to find the range, you simply find the area of a cube with a side of 3 (the smallest one you can have), and that tells me that my range has to be greater than or equal to 54.  

There are different notations for identifying domain and range. There is the set-builder notation and the interval notation:

Set-builder:

 

Interval: ( a, b)

Also, for those of you who are more visual learners, here is a graph with the domain and range specified after: 

Domain: (negative infinity, infinity) because the graph stretches out on the x-axis.

Range: (-3, infinity)

If you have any questions please let me know and have a wonderful weekend!