Doing some pre calc can anyone explain a function that has a domain of all real numbers, but a range of integers and why? Pic related is closest I could come up with
Doing some pre calc can anyone explain a function that has a domain of all real numbers...
[math]f(x)=ceil(x)[/math]
What do you mean explain? Explain what that is? It means a function that you can input any real number and any answer you get out will be an integer. Example:
f(x) = 0^x
0 to any power is 1, 1 is an integer. Domain is all real numbers, range is 1.
floor and ceiling functions
x^2 still includes elements of the real numbers greater than 0
wait, I just fucked that up because 0 isn't in the domain. here
f(x) = 1
let me rephrase, it includes all real numbers greater than 0
f(x)=x if x is an integer, 0 if not
I have no clue what floor and ceiling functions are
Needs to be all real numbers.
Here's another brain teaser: what's a function who's domain is all real numbers, but is not a continuous function. I'm guessing some type of piecewise function
Step function. Look up step function and heaviside function.
For my first question or
There are functions that can approach a certain y value but never actually reach it. These are called horizontal asymptotes.
Is that like y=1/x?
f(x)=ax/x
where: a is any integer
that was perfectly fine until you put the x/x there you dingus
Yeah, but that's a vertical asymptote. x = 0 is not defined and y approaches either positive or negative infinity as x approaches 0 (depending on from which direction).
This thread isn't good enough, let me propose a better question: Is there a function f: RxR -> R such that f is continuous on every horizontal slice of RxR (the lines (x,y_0)), in the single variable sense, and on every vertical slice of RxR (the lines (x_0, y)), in the single variable sense, but f: RxR -> R is not continuous in the multivariable sense at at least one point?
Both, especially the first one
Don't worry about it OP, functions like that are pretty irregular.
>range
By range do you mean the image set?