Domain and range are often confused by students. Let's start with the basic definitions (always a good thing to do).

The domain is the set of all first elements of ordered pairs (

The range is the set of all second elements of ordered pairs (

Let's take a simple example. What is the domain and range for points {(2,5), (4,8), (-2,1), (-3,-5)}?

Well, the set of x coordinates is {2,4,-2,-3} and the set of y coordinates is {5,8,1,-5}.

So the domain of these ordered pairs is {2,4,-2,-3} and the range is {5,8,1,-5}.

What about the domain of range of y = x^2 + 2?

The domain is the set of all first elements of ordered pairs (

*x*-coordinates).The range is the set of all second elements of ordered pairs (

*y*-coordinates).Let's take a simple example. What is the domain and range for points {(2,5), (4,8), (-2,1), (-3,-5)}?

Well, the set of x coordinates is {2,4,-2,-3} and the set of y coordinates is {5,8,1,-5}.

So the domain of these ordered pairs is {2,4,-2,-3} and the range is {5,8,1,-5}.

What about the domain of range of y = x^2 + 2?

Answer: To answer this, we have to find the domain of x values. Which x values work for this equation? The answer is all x values of real numbers, so the domain is all Real Numbers! What about the range? What is the lowest value of y? It is 2, when x = 0, because for all other values of x, whether negative or position, y is always greater than 2. Try it out yourself. See the graph for help and details. So the range is y >= 2. Final answer: Domain is all real numbers and range is y >=2. | Graph of y = x^2 + 2 |