SOLUTION: Hi there. I need to see if I am on the right track. I need to graph the following y = -2 abs(x+1)-4. I need to construc a sequence of five graphs to get from one to another.

Algebra ->  Graphs -> SOLUTION: Hi there. I need to see if I am on the right track. I need to graph the following y = -2 abs(x+1)-4. I need to construc a sequence of five graphs to get from one to another.       Log On


   

Question 212735: Hi there. I need to see if I am on the right track. I need to graph the following y = -2 abs(x+1)-4. I need to construc a sequence of five graphs to get from one to another.
I am setting up my 5 graphs as follows: (1) y = abs(x) (2) y = abs(x+1)
(3) y = -2 abs (x+1) (4) y = 2 abs (x+1) and (5) y = -2 abs (x+1)-4.
Am I on the right track with the above equations?
Thanks - Lori
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
To graph y=-2%2Aabs%28x%2B1%29-4, simply follow the given steps below:


Step 1) Graph y=abs%28x%29

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+abs%28x%29%29+ Graph of y=abs%28x%29

Note: the graph of abs%28x%29 is simply comprised of the lines y=x and y=-x (just don't graph the portion that lies below the x-axis).


Step 2) Shift y=abs%28x%29 1 unit to the left to get y=abs%28x%2B1%29

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+abs%28x%29%2Cabs%28x%2B1%29%29+ Graph of y=abs%28x%29 (red) and y=abs%28x%2B1%29 (green)


Step 3) Vertically stretch y=abs%28x%2B1%29 by a factor of 2 to get y=2abs%28x%2B1%29


+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+abs%28x%2B1%29%2C2%2Aabs%28x%2B1%29%29+ Graph of y=abs%28x%2B1%29 (red) and y=2%2Aabs%28x%2B1%29 (green)


Step 4) Reflect y=2abs%28x%2B1%29 over the x axis to get y=-2%2Aabs%28x%2B1%29


Graph of y=2%2Aabs%28x%2B1%29 (red) and y=-2%2Aabs%28x%2B1%29 (green)


Step 5) Shift the entire graph of y=-2%2Aabs%28x%2B1%29 down 4 units to get y=-2%2Aabs%28x%2B1%29-4


Graph of y=-2%2Aabs%28x%2B1%29 (red) and y=-2%2Aabs%28x%2B1%29-4 (green)




So the graph of y=-2%2Aabs%28x%2B1%29-4 is

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+10%2C+-2%2Aabs%28x%2B1%29-4%29+ Graph of y=-2%2Aabs%28x%2B1%29-4