f (x)= x^2 + 6
Recall that for a function f defined by an expression in terms of a variable x, the domain of f is the set of all real numbers x can take such that the expression defining the function is real. The range of f is the set of all values that the function takes when x takes the values given in the domain.
f(x) = x2 + 6
Notice that a valid output will be produced for any x-value plugged into the expression defining f(x). Thus, the domain of this function is all real numbers x, which in interval notation is given by the following:
Domain : (-∞, ∞)
Since this function is a quadratic function, its graph will be a parabola which will open upwards since the leading coefficient is positive. Being that it opens upwards, it will have a minimum y-value of 6. Therefore, the range is all y-values that are greater or equal to 6 (i.e., f(x) ≥ 6). In interval notation, the range is as follows:
Range: [6, ∞)