SOLUTION: Consider the parent function f(x)= √x. What parameters (a, k, d, c) affect the domain of g(x)= af[k(x-d)] + c? Explain.

The domain of the parent function is the set of all non-negative real numbers.



Of the listed parameters,  "a" and "c" DO NOT affect the domain of the "child" function,

while parameters "k" and "d" DO affect.



According to the definition of the square root, the aggregated value k*(x-d) must be non-negative.


It implies that


    a)  if k > 0, then   x >= d

    b)  if k < 0, then   x <= d

    c)  if k = 0, then x can be any real number.