Doing some pre calc can anyone explain a function that has a domain of all real numbers...

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

[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?

google

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?