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

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Question 155782: Graph the follwing functions:

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

Note: the expression abs%28x%2B2%29 can be broken into the expressions %28x%2B2%29 and -%28x%2B2%29=-x-2

y=-abs%28x%2B2%29%2B10 Start with the given equation


y=-%28x%2B2%29%2B10 Replace abs%28x%2B2%29 with %28x%2B2%29


y=-x-2%2B10 Distribute


y=-x%2B8 Combine like terms.


Now graph y=-x%2B8


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-x%2B8%29 Graph of y=-x%2B8


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y=-abs%28x%2B2%29%2B10 Start with the given equation


y=-%28-x-2%29%2B10 Replace abs%28x%2B2%29 with %28-x-2%29


y=x%2B2%2B10 Distribute


y=x%2B12 Combine like terms.


Now graph y=x%2B12


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2Cx%2B12%29 Graph of y=x%2B12


So together the graphs are


graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-x%2B8%2Cx%2B12%29 Graph of y=-x%2B8 (red) and graph of y=x%2B12 (green)


Since the leading sign on the absolute value is negative, this means that we'll erase the upper portion of the graph and keep the bottom portion like this:



graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-abs%28x%2B2%29%2B10%29 Graph of y=-abs%28x%2B2%29%2B10



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Answer:

So the graph of y=-abs%28x%2B2%29%2B10 is

graph%28500%2C500%2C-10%2C10%2C-8%2C12%2C-abs%28x%2B2%29%2B10%29