Domain and Range

The domain of a function is the set of all possible input values for which the function is defined. The range of a function is a set of all possible output values that the function can produce. Let’s take a look at figure 2 below.

domain and range

The function represented in figure 2 has the equation f(x) = 2x+1. What would the domain of this function be?

Well, if you notice, it does not matter what value of x we select. We will always get a defined value for the output. So, we can say that the domain of f(x) = 2x + 1 is all real numbers. This is how you would write this:

Domain: -∞ < x < ∞  or (-∞,∞)

So now, what would the range of the function be? We can see in figure 2 that the function can take on any value. This means that the range is:

Range: (-∞,∞)

The function we just found the domain and range for is a simple polynomial. However, finding the domain and range for many other types of functions is a bit more difficult. We will explore these functions in the coming sections.

Note:

The domain is a set of all defined inputs and the range is a set of all possible outputs corresponding to the inputs in the domain

Try the examples below. We suggest use a graphing tool such as Desmos to help you visualize the functions!

What is the domain and range of the function f(x) = x²

State the Domain and Range of the function f(x) = x³

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