SOLUTION: Graph the follwing functions: B) y= -|x+10|-2

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Question 155778: Graph the follwing functions:

B) y= -|x+10|-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Remember, if abs%28x%29=A, then x=A or x=-A. So this means that abs%28x%2B10%29 can be broken up into %28x%2B10%29 and -%28x%2B10%29=-x-10


y=-abs%28x%2B10%29-2 Start with the given equation


y=-%28x%2B10%29-2 Replace abs%28x%2B10%29 with %28x%2B10%29


y=-x-10-2 Distribute


y=-x-12 Combine like terms.


Now let's graph y=-x-12


graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-x-12%29 Graph of y=-x-12


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y=-abs%28x%2B10%29-2 Start with the given equation


y=-%28-x-10%29-2 Replace abs%28x%2B10%29 with %28-x-10%29


y=x%2B10-2 Distribute


y=x%2B8 Combine like terms.


Now let's graph y=x%2B8


graph%28500%2C500%2C-15%2C5%2C-12%2C8%2Cx%2B8%29 Graph of y=x%2B8


Now let's graph the two equations on the same coordinate system:


graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-x-12%2Cx%2B8%29 Graph of y=-x-12 (red). Graph of y=x%2B8 (green)


Now since the sign in front of the absolute value is negative, this means that we only need to worry about the negative portion. So this means that we have to erase the portions of the graph that are above the intersection like this:


graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-abs%28x%2B10%29-2%29 Graph of y=-abs%28x%2B10%29-2


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Answer:

So the graph of y=-abs%28x%2B10%29-2 is

graph%28500%2C500%2C-15%2C5%2C-12%2C8%2C-abs%28x%2B10%29-2%29