Final answer:
The domain of the function f(x) = 5| x - 2 | + 4 is all real numbers, and the range is [4, infinity).
Step-by-step explanation:
The function in question is f(x) = 5| x - 2 | + 4. To find the domain and range of this function, let's consider the properties of absolute value functions and linear transformations.
The domain of an absolute value function is all real numbers because you can take the absolute value of any real number. Therefore, for the given function, the domain is also all real numbers, which can be represented as (-∞, ∞).
The range of the function is determined by looking at the transformation applied to the basic absolute value function. Since the absolute value is multiplied by 5, the lowest value it can take is 0 (when x=2). Adding 4 to this, the minimum value of the function becomes 4. Because there is no upper limit to how large the absolute value can be, there is no upper limit for this function after scaling and translation. Therefore, the range of the function is [4, ∞).