SOLUTION: I really could use some help with this one. "Sketch using transformations: f(x) = -2|x+2|. Start with the basic graph and show all stages." I know that there are supposed to be

Algebra ->  Functions -> SOLUTION: I really could use some help with this one. "Sketch using transformations: f(x) = -2|x+2|. Start with the basic graph and show all stages." I know that there are supposed to be      Log On


   

Question 64617: I really could use some help with this one.
"Sketch using transformations: f(x) = -2|x+2|. Start with the basic graph and show all stages."
I know that there are supposed to be four graphs, but I just don't understand this, please help!
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
I really could use some help with this one.
"Sketch using transformations: f(x) = -2|x+2|. Start with the basic graph and show all stages."
IN PROBLEMS INVOLVING ABSOLUTE VALUES |F(X|..HERE...|X+2|,YOU HAVE TO CONSIDER 2 CASES
1.WHEN X+2>=0.....THAT IS X>=-2.....THEN|X+2|=X+2
2.WHEN X+2<=0.....THAT IS X<=-2.....THEN |X+2|=-(X+2)=-X-2.
THAT IS ALL.
FOR CASE 1.
WE HAVE GRAPH EQN. AS
Y=-2(X+2).......FOR X>=-2
X=........-2........0...................5...........10......ETC
Y=X+2......0........-4..................-14.........-24......ETC.
PLOT THESE POINTS TO GET THE GRAPH.
+graph%28+500%2C+500%2C+-2%2C+10%2C+-30%2C+0%2C+-2%28x%2B2%29%29+
FOR CASE 2.
WE HAVE EQN. OF GRAPH AS
Y=-2(-X-2)=2(X+2)...........FOR X<=-2
X=..............-10............-5..............-2
Y=2(X+2)=.......-16............-6..............0
PLOT THE POINTS TO GET THE GRAPH . IT WILL LOOK AS SHOWN BELOW.
+graph%28+500%2C+500%2C+-10%2C+-2%2C+-10%2C+10%2C+2%28x%2B2%29%29+
YOU MAY PLOT BOTH ON SAME GRAPH,THOUGH I SHOWED 2 GRAPHS
IT WILL BE AN INVERTED V WITH VERTEX OR MAXIMUM AS Y=0 AT X=-2 AND GOING FURTHER NEGATIVE AS X INCREASES OR DECREASES.
I know that there are supposed to be four graphs, but I just don't understand this, please help!