This was on my Pre-Cal test. I want to see what the VGC community thinks.

abs(X-2)+abs(X+2)-abs(X-5) = y

Basically a piecewise graph.

Simplify the expression and give the conditions on which its slope changes or whatever.

A graph would be nice, but you don't have to post it.

Hey man, hope your test went well.

With these types of questions you have to identify the points at which the signs inside the absolute values change, which gives you your continuos intervals.  So looking at the absolute values, we see that the intervals are:

-infinity <= x < -2    ,    -2 <= x <= 2    ,  2 < x <= 5    and:    5 < x <= infinity.

At the places where the intervals meet, there will be a "corner" of your graph, where the slope changes.

Now you just have to simplify the expression for each of these intervals by assigning values to the absolute value equations.  I'll do a couple for ya, but its not really that complicated.

On the interval from -infinity to -2:  (2-x) plus (-2-x) - (5-x) = y                simplifies to:   -x - 5 = y

On -2<x<2:   (2-x) plus (x plus 2) - (5-x) = y                                                   simplifies to : -1 plus x = y

On 2<x<5:  (x-2) plus  (x plus 2) - (x-5) = y                                                     simplifies to :  3x - 5 = y

If you plot these, you will get a graph of your function.

I'll leave the last one for ya.  The main idea is to understand where the numbers inside the absolute values change signs, and those are the intervals of continuity. This is a fairly time consuming question if you're not confident with absolute value functions.

Best of luck with the rest of your term.

Edit: fixed missing operators.  Also realized that it is hard to explain these things over the internet without going into lengthly detail... sorry about the shitty explanation.  Best bet is to review Absolute value functions.

What is "abs?"

Muscle math?

EDIT: Oh, absolutes. Damn i've forgotten a lot since Calculus.

This just made me realise how long it is since I have studied maths, and I used to be good at it.

i have no idea

luckily i left tests along time ago,but good luck with it

Anti-lock braking system

What's abs?

Edit: Mr. Khan ninjed me.

Edit 2.0: even with the explanation, I still have absolutely no idea what this is about.

Why are we talking about math on VGChartz?

...I mean unneeded math. Calculating sales is okay since it's applied and not pointless....

Is easy, just put it into excel.

Column A is x

Column B is y

x should vary from about -6 to 8 or so

y should be calculated using =ABS(A2-2) ABS(A2 2)-ABS(A2-5), where A2 is the relevant x value for the Y value in question

Edit - did not realise you were discussing this in the context of a test. Epoch's response is thus much more useful than mine.

If something like this comes up in an exam (trying to graph a function that you don't know how to graph), I find the best option is to substitute various values of x into the equation. and calculate y, then start your graph by plotting these points, keep plotting mroe and more points until the pattern becomes obvious and then play connect the dots

EDIT: Had to break the link, the HTML renderer fucks it up

http://www.wolframalpha.com/input/?i=abs(X-2)+abs(X+2)-abs(X-5) = y