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

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Question 155779: Graph the follwing functions:

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

If abs%28x%29=A, then x=A or x=-A. So this tells us that abs%28x-2%29 can be broken up into %28x-2%29 and -%28x-2%29=-x%2B2


y=-abs%28x-2%29-10 Start with the given equation


y=-%28x-2%29-10 Replace abs%28x-2%29 with the first portion %28x-2%29


y=-x%2B2-10 Distribute


y=-x-8 Combine like terms.


Now graph y=-x-8


graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-x-8%29 Graph of y=-x-8


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y=-abs%28x-2%29-10 Start with the given equation


y=-%28-x%2B2%29-10 Replace abs%28x-2%29 with the second portion %28-x%2B2%29


y=x-2-10 Distribute


y=x-12 Combine like terms.


Now graph y=x-12


graph%28500%2C500%2C-10%2C10%2C-15%2C5%2Cx-12%29 Graph of y=x-12


Now graph the two equations together:

graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-x-8%2Cx-12%29 Graph of y=-x-8 (red). Graph of y=x-12 (green)


Once again, since the sign out front the absolute value is negative, this means that the portion we keep is the negative portion that is below the point of intersection like this:


graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-abs%28x-2%29-10%29



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Answer:

So the graph of y=-abs%28x-2%29-10 is

graph%28500%2C500%2C-10%2C10%2C-15%2C5%2C-abs%28x-2%29-10%29