1. ## Methods of graphing

I've been given a rather bizarre homework assignment. some of the problems involve graphing. Like this one:

$y = \mid {x+1} \mid + \mid {x+2} \mid$

I can just plot points, but that is too time consuming. I've been told about a method of graphing them separately and adding them together, I forget exactly what it was, but it's a different method of graphing. Is there someone that knows it?

Then the homework assignment starts to become very strange when we are given to graph this:

$[x^2 + y^2 - 1] [y - x + \frac {0}{\sqrt{-x}}] [y - \sin (x) + \frac {0 \sqrt{x -2\pi}}{\sqrt{4\pi - x}}]$

How in the world am I supposed to graph this? To be honest, I was really intimidated when seeing this problem.

2. Originally Posted by >_<SHY_GUY>_<
$y = \mid {x+1} \mid + \mid {x+2} \mid$

I can just plot points, but that is too time consuming. I've been told about a method of graphing them separately and adding them together, I forget exactly what it was, but it's a different method of graphing. Is there someone that knows it?
Its called the addition of ordinates which involves taking the the points from either function and adding them together. You only need to take a few to get the general shape in most cases. You can also use limits.

3. Originally Posted by pickslides
Its called the addition of ordinates which involves taking the the points from either function and adding them together. You only need to take a few to get the general shape in most cases. You can also use limits.
and it wouldn't matter if there was something else added to the same equation. For example, if there was a | x |, then I would still have to add the points from all three, correct?

4. Yep...

5. Originally Posted by >_<SHY_GUY>_<
I've been given a rather bizarre homework assignment. some of the problems involve graphing. Like this one:

$y = \mid {x+1} \mid + \mid {x+2} \mid$

I can just plot points, but that is too time consuming. I've been told about a method of graphing them separately and adding them together, I forget exactly what it was, but it's a different method of graphing. Is there someone that knows it?
For this particular problem, where you have absolute value signs, you can just break it into pieces as you do all absolute value problems. If x< -2, both x+1 and x+ 2 are negative so y= -(x+1)- (x+ 2)= -2x -3, a straight line. if -2< x< -1, x+ 1 is still negative but x+ 1 is positive so y= x+1- (x+ 2)= 1- 2= -1, a horizontal straight line. If x> -1 both x+ 2 and x+ 1 are positive so y= x+ 1+ x+ 2= 2x+ 3, again a straight line. You graph is a line descending from the left to (-2, -3), the horizontal line from (-2, -3) to (-1, -3) then a straight line ascending to the right from (-1, -3).

Then the homework assignment starts to become very strange when we are given to graph this:

$[x^2 + y^2 - 1] [y - x + \frac {0}{\sqrt{-x}}] [y - \sin (x) + \frac {0 \sqrt{x -2\pi}}{\sqrt{4\pi - x}}]$
I have no idea what that means. Why do you have those "0"s in there?

How in the world am I supposed to graph this? To be honest, I was really intimidated when seeing this problem.
I recommend a graphing calculator!