Summer Math Work! Need Help.


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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.

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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)

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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

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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.

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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!

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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...

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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.

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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!

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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?

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