I think confusion can arise if you are not clear what function you refer to. As you define f its domain is [-2, 1]]. You are defining a new function as a transformation of f, that is g(x) = f(x-1) + 1. The domain of f remains the same, but the domain of g is [-1, 2] since these are the input values for the independent variable of g that are allowable.
Alan Lipp Williston Northampton School
On Sep 14, 2012, at 8:54 AM, Michael Ecsedy wrote:
> Hi, all. This doesn't really pertain to Calculus, but I noticed this when I was teaching Algebra today and thought I could get some expert opinion from you all. I drew a graph of f(x) which I defined for -2?x?1. I then had the students draw the graph of f(x-1)+1. We currently teach in Algebra that you can determine the domain of a function from a graph by looking at what values of "x" are covered. I realized that if I had asked them a domain question at that point, they would have said the domain is -1?x?2. Is it correct to say that the domain is the set of acceptable values for "x" (in this case -2?x?1), or is it correct to say that the domain is the set of values that the function is performed on (in this case -1?x?2) ? Or do we just have to be more careful when we teach that you can determine the domain from the graph the way we do. Thank you, Mike Ecsedy, Joel Barlow HS, Redding, CT > ==== > Course related websites: > http://apcentral.collegeboard.com/calculusab > http://apcentral.collegeboard.com/calculusbc > To search the list archives for previous posts go to > http://lyris.collegeboard.com/read/?forum=ap-calculus >