Question 716047: how do you graph Y=|x|-2
i need help
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! 
For  --> 
That gives you one point of the graph, point (0,-2).
You can always calculate more points to get a graph,
but thinking and planning ahead may save you some work.
Knowledge and prior experience helps too.
NOTE: If your teacher expects a table showing the x and y values for points on the graph that you calculate, do not forget to include a table. If the format of the table is important to your teacher, pay attention to the format. Also pay attention to the way your teacher wants you to mark, or not to mark points on the graph. I like to make little circles around points I calculate and plot on the graph, but If I had a teacher that likes little crosses, or that likes no marks at all, I would do as the teacher wants.
IF YOU KNOW ABOUT SYMMETRY IN FUNCTIONS
You would realize that gives the same  value
to opposite values for  because  .
Then you would only need to worry about graphing the part for 
knowing that the other side of the graph is symmetrical.
IF YOU KNOW ABOUT ABSOLUTE VALUE FUNCTION
You would know what the graph of  looks like, 
and realize that for every
is  less than ,
you would just draw the graph
as for , but moved 2 units down 
IF YOU KNOW ABOUT LINEAR FUNCTIONS
You would notice that for the graph of the function is the same as
 .
is the equation of a straight line in slope-intercept form.
The slope is that invisible  in front of the
and the y-intercept is That  at the end, telling you that the line gets to the y-axis at point (0,-2).
With a slope of you would know that as x increases by ,
also increases by ,
and from point (0,-2) you would go to (1,-1),and then to (2,0), and then to (3,1), and so on.
You may like to mark points on the graph like that.
Or maybe you would just want to calculate and plot two points and connect them with a line.
In that case, (0,-2) is an obvious point, and then you could calculate, say
for  ,  to get point (6,4).
Either way, you would get the line you need for
That would give you half of the graph 
Hopefully you would realize that the graph is symmetrical.
Otherwise, for  , where the function is 
you would be working in a similar manner to draw the other line.
You may mark points based on a slope of  by going
spaces to the right (that is 1 space to the left) and
space up as you go from point to point,
(0,-2) --> (-1,-1) --> (-2,0) --> (-3,1) and so on.
Or maybe you would calculate point (-7,5) by making
 and calculating 
Either way you would get 
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