hifive Posted June 20, 2004 Share Posted June 20, 2004 I just receieved my summer work in the mail for AP Calculus. It doesn't seem hard, but this period of nothing has really bogged me down, and I don't remember much at all. So I need help: What does it mean if a function is periodic? y = sec (x) --- What is the Domain and Range of this function? y = log x / log 2 --- Domain and Range y = 1/x --- Domain and Range y = 1/(x^2) --- Domain and Range I hate functions. This is the only stuff that I'm having problems with. So anyone? Thanks. Link to comment Share on other sites More sharing options...
mr.dan Posted June 20, 2004 Share Posted June 20, 2004 can't find my graphing calc at the moment. Link to comment Share on other sites More sharing options...
sciguy007 Posted June 20, 2004 Share Posted June 20, 2004 a periodic function repeats itself over a given "period" or distance. sin(x) is periodic for example. sec(x)=1/cos(x), so when cos(x)=0, the function is undefined. thus the range is all real x except (2*k-1)*pi/2, where k is any integer. the domain is (1,infinite) and (-infinite,-1) y=log(x)/log(2), domain is 1 to infinite, since log 1=0, range is something you can calculate because im lazy. y=1/x, domain is all x but zero, range is (-infinite,infinite) y=1/(x^2), same as above for domain, range is (0,infinite) i kinda whipped that out kinda fast, so check my answers edit: range of y=log(x)/log(2) is [0,infinite) Link to comment Share on other sites More sharing options...
Mike Posted June 20, 2004 Share Posted June 20, 2004 i think a periodic function is one that produces a graph which effectively loops (like sin & cos graphs) domain & range are to do with what x and y can be but not sure which way it is Link to comment Share on other sites More sharing options...
incubusdaemon Posted June 20, 2004 Share Posted June 20, 2004 a periodic function repeats itself over a given "period" or distance. sin(x) is periodic for example.sec(x)=1/cos(x), so when cos(x)=0, the function is undefined. thus the range is all real x except (2*k-1)*pi/2, where k is any integer. the domain is (1,infinite) and (-infinite,-1) y=log(x)/log(2), domain is 1 to infinite, since log 1=0, range is something you can calculate because im lazy. y=1/x, domain is all x but zero, range is (-infinite,infinite) y=1/(x^2), same as above for domain, range is (0,infinite) i kinda whipped that out kinda fast, so check my answers edit: range of y=log(x)/log(2) is [0,infinite) The quoted part above is true if and only if x,y spans the set of all real numbers. If you are allowing complex numbers (those including i = sqrt(-1)) then the answer is different. For example, log of negative numbers is complex. Since it's AP calculus, it's most likely just real numbers. Link to comment Share on other sites More sharing options...
hifive Posted June 20, 2004 Author Share Posted June 20, 2004 Only Real Numbers; No Imaginary Numbers. Thanks a lot! Link to comment Share on other sites More sharing options...
hifive Posted June 20, 2004 Author Share Posted June 20, 2004 I think these may be wrong: y=1/x, domain is all x but zero, range is (-infinite,infinite)Isn't range (-infinite, 0) (0, infinite)?edit: range of y=log(x)/log(2) is [0,infinite) Isn't range (-infinite, infinite)? And one more. What is the domain and range of y = [x]? Thanks! Link to comment Share on other sites More sharing options...
trek Posted June 21, 2004 Share Posted June 21, 2004 edit: nm. Link to comment Share on other sites More sharing options...
sciguy007 Posted June 21, 2004 Share Posted June 21, 2004 sorry, had some stuff backwards y=1/x: domain is all real x but 0, range is (-infinite, 0) (0, infinite) y=log(x)/log(2): domain is (0,infinite), range is (-infinite,infinite) i think thats right, its been a while since ive done this stuff so im rusty... Link to comment Share on other sites More sharing options...
hifive Posted June 21, 2004 Author Share Posted June 21, 2004 Haha. No Problem. I'm almost done! Just one last Q: Is there a characterstic of a function that assures that its reflection across the line y = x is a function? I put: No Identifying Characteristic. Link to comment Share on other sites More sharing options...
hifive Posted June 21, 2004 Author Share Posted June 21, 2004 Please help me out with this last question!: Is there a characterstic of a function that assures that its reflection across the line y = x is a function? Thank You So Much! Link to comment Share on other sites More sharing options...
incubusdaemon Posted June 21, 2004 Share Posted June 21, 2004 Since reflection over x=y is the same as turning y(x) into it's inverse x(y), the original function y(x) would have to be single-valued for all y. (i.e. a line would work, as for every value of y, there is only one value of x. A parabola doesn't- if y(x) = x^2, y=4 has 2 values of x- -2 and 2, so it's inverse isn't a function). Does that make sense? Link to comment Share on other sites More sharing options...
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