Question 216470: what is the absolute value function of y=-|x|+1 how do i graph it?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! There are a couple of ways we can graph this.
Solution 1: If you know what the graph of  then you can figure out  :- The "-" in front of the absolute value causes the graph to be reflected in the x-axis.
- The "+1" causes the graph to be raised up 1 unit.
- Putting these together, the graph of is the graph of reflected in the x-axis and then raised up 1.
Solution 2: Use what you know about absolute value to rewrite as a piecewise function. (This will make more sense when you see it.) What do we know about absolute value? We know that- The absolute value of any positive number is itself.
- The absolute value of zero is itself
- The absolute value of any negative number is the negative of its negative self (IOW, the "positive version" of itself)
To put this in algebraic terms:
If  then 
If  then 
Now we can use these to rewrite in two ways, one for and another for :
If then 
If then 
And we can use these to graph . On a graph is on the y-axis and to the right of the y-axis and is to the left of the y-axis. So we graph , which is a simple line (slope = -1, y-intercept = 1) just from the y-axis and to the right. And then, on the same graph, graph  , which is also a simple line (slope = 1, y-intercept of 1), just to the left of the y-axis.
Either way we should end up with a graph that looks somewhat like an upside down "v" with the point of the "v" at (0,1).
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