what is the domain and range of f(x) = x^2?
To find the domain and range of a function, we need to understand what these terms mean.
The domain of a function is the set of all possible input values (x-values) for which the function is defined. In other words, it is the set of values that we can substitute into the function to get meaningful outputs.
The range of a function is the set of all possible output values (y-values) that the function can produce. It represents the set of values that the function takes on as its inputs vary.
For the function f(x) = x^2, we can determine the domain and range as follows:
1. Domain:
Since we can square any real number, there are no restrictions on the input values (x-values) for this function. Therefore, the domain of f(x) = x^2 is all real numbers.
Domain: (-∞, +∞) or (-∞, +∞)
2. Range:
To determine the range, we need to consider the possible output values of the function.
When we square any real number, the result will always be a non-negative number (including zero). This means that the function f(x) = x^2 can never produce negative outputs.
So, the range of f(x) = x^2 consists of all non-negative real numbers.
Range: [0, +∞) or [0, +∞)
In summary:
Domain: (-∞, +∞)
Range: [0, +∞)