Answer:
Domain is all the possible x-values a function can have. For example, for the function f(x) = √x, the domain would be x ≥ 0, because you cannot square a negative number. Another example is the function g(x) = 2x. The domain of g(x) would be all real numbers, or ℝ.
Range is all possible y-values a function can have. For example, for the function f(x) = √x, the range would be f(x) ≥ 0, since the square root of a number will be positive. Another example is h(x) = x². The square of x will not be negative, so the range of h(x) will be h(x) ≥ 0.
For functions of the parent family y = a(x - h)² + k, the domain and range will always be⇒ Domain: all real numbers, and Range: y ≥ k
For functions of the parent family y = a(x - h)³ + k, the domain and range will always be all real numbers.
For functions of the parent family y = a√(x - h) + k, the domain and range will always be⇒ Domain: x ≥ h, and Range: y ≥ k
For functions of the parent family y = a∛(x - h) + k, the domain and range will always be all real numbers.
