Find the domain and range of
h(y)=-3sqrt(14 + 3y). The answer on Paul's Online Notes makes absolutely no sense, so I need an alternate explanation for how to do this.

Question

Find the domain and range of 
h(y)=-3sqrt(14 + 3y). The answer on Paul's Online Notes makes absolutely no sense, so I need an alternate explanation for how to do this.

nory · Answer

Domain: Domain is all the values that have a defined value of h(y). Basically, no dividing by zero, no square roots of negatives, etc.
Because 14 + 3y must be equal to or greater than 0, find all the values that make it equal/greater than 0.

anonymous · Answer

So that just gets me to y is greater than or equal to -14/3. According to Paul's online Notes, this means that the domain is [-14/3, infinity). How is this the domain?

nory · Answer

Because those are all the values the function will allow without becoming undefined. The domain can't have any numbers that make the square root negative, and those are all the numbers that make the number under the square root zero or greater. Do you see? If not, I can explain more.

anonymous · Answer

OH ok I see it now. And as for the range, since the equation is a modification to a basic line (14 + 3y) shouldn't the range then be all real numbers?

nory · Answer

That's not the way I learned it. But it's possible. If you can get your hands on a copy of the graph, you can see the range visually.

anonymous · Answer

For domain and range questions, do you recommend simply inputting the function into a graphing calculator every time and inferring the answer from the displayed graph, or taking the time to find the domain and range algebraically?

nory · Answer

No--algebra! This is the method teachers like to teach you in case you don't have a graphing calculator on hand. The algebra method is definitely more difficult, but you should probably practice it that way.