Help on a piecewise function!

Consider the graph to be two parts. The key to this is the absolute value of x.

Graph the equation for positive values of x; and then graph the equation for negative values of x.

I assume you meant |x|, not [x], right? That is, the absolute value of x?

Think of what that means. That means that for values of X that are less than 0, the function is equivalent to y = -x + 2. And for values of X that are greater than 0, the function is equivalent to y = x + 2. So graph those two equations for their respective ranges.

No it isn’t absolute value, it’s something else! :/ It makes no sense haha!

Then you need to tell us what the “something else” is.

Did your teacher or your textbook say anything about what [x] is supposed to mean? That is not standard notation for any operation that I know of.

Well I don’t really understand this but my teacher wrote this on the board:

y=[x] “y is the greatest integer less than or equal to 0”

Are you talking about the floor function? Those aren’t brackets, those are… well, there aren’t keys for them on a standard keyboard. Basically, they look like brackets without the top horizontal marks. But it wouldn’t be “the greatest integer less than or equal to 0”, it’d be ”... less than or equal to x”.

So if
y = floor(x)

then for any x between 1.0000000 and 1.9999999<etc>, y = 1.
for any x between 2.0000000 and 2.999999999<etc>, y = 2.
and so on and so on.

To draw a graph of y=floor(x), you would draw a horizontal line between (0,0) and (1,0); between (1,1) and (2,1); between (2,2) and (3,2); etc. For each line, you make the rightmost portion of the line an open circle, to indicate that the line doesn’t actually include that terminal point.

If that doesn’t make a whole lot of sense, try this site that might explain it better than I did: http://www.mathsisfun.com/sets/function-floor-ceiling.html

The [bracket] notation was actually the standard for denoting the floor function until the “ceiling” function was introduced in 1962.

Basically, for nonnegative real numbers, you truncate the fractional part of the number, leaving the whole number. For example, the floor of 2.741 would be 2, since the numbers after the decimal are “chopped off.”

For each integer n, draw a line between the points (n, n+2) and (n+1, n+2).