One question on my take-home exam is this:
For each of the following types of functions, give an example in algebraic form f(x)= (insert function), then sketch the graph and describe the domain and range.
I've got an example of each function asked of me (linear, constant, quadratic, radical, exponential, logarithmic) and I've also done the graph of each. I know what domain and range is but "describe" it? I emailed my prof. asking her what exactly does she mean by "describe it" and she said; "Interval notation for the domain and range is one form of a good description. (Set builder notation and verbal descriptions can also work.)
I must admit that putting domain and range in interval notation is not my strong point. So that is what I'd like help with.
If it helps, here are the examples I used:
Linear f(x) = 2x+4
Constant f(x) = 2
Quadratic f(x) = -x^2+2x+3
Radical f(x) = square-root(3-x) (I'm sorry I don't know the command for square root).
Exponential f(x) = 2^x
Logarithmic f(x) = log 2^x (again sorry for not knowing the command to display the 2 lower than the log).
If anyone is able to help me understand how to find the interval notation from these examples that would be super-amazing-great. My favorite math site, Purple Math, isn't as helpful as usual with this subject. My 75 dollar online textbook requires me to basically read a book just to figure out one thing.
Thanks in advance and sorry again for my MathHelpForum newbieness.
Edit: If you'd prefer to talk about set builder notation and/or verbal descriptions that would be helpful as well, as my prof. said those were acceptable methods too. I chose interval notation because I think that's her favorite.