Question

Which of the following could be an example of a function with a domain

Answer 1

D)

For that square root to be a valid thing, the expression it is applied to has to be greater or equal to 0. Ergo, the condition on the domain (values which x can take) is that (x-a) >= 0, thus x has to have values between [a,infinity) for that expression to be valid.

And of course, since it's a continuous monotonic increasing function (the first derivative will forver be positive and it has no global/local points of extreme minimum/maximum), the lowest value it can possibly take is b (when x=a) and then it goes on to infinity - so the range is [b,infinity).

Answer 2

yea thanks! i figured it out :)