2. DOMAIN AND RANGE: what is the domain and range of the function f(x) = x²

Answer 1

As a reminder:

The domain is the set of all possible values for which the function is defined, and the range is the set of all possible outputs of a function.

Now knowing this, let's find the domain and range of f(x) = x².

Since this function is quite simple, you can easily graph the function and find the domain and range.

However, a common way to find the domain and range is to plug in points for the f(x) and create a table.

I have created a simple table below of f(x) = x² and will observe the pattern in order to determine the domain and range:

x: -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

f(x): 36 25 16 9 4 1 0 1 4 9 16 25 36

Based on this table, we can conclude that the domain is all real numbers, since the values of f(x) are increasing exponentially for every input, and the range is all values greater than or equal to 0, since the values of f(x) are greater than or equal to 0 even when the input is a negative value.

Final answer:

Domain: (-∞, ∞)

Range: [0, ∞)