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

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Question 155777: Graph the follwing functions:

A) 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-10%29 can be broken up into %28x-10%29 and -%28x-10%29=-x%2B10

y=-abs%28x-10%29%2B2 Start with the given equation


y=-%28x-10%29%2B2 Replace abs%28x-10%29 with %28x-10%29 (which is the first part)


y=-x%2B10%2B2 Distribute the negative.


y=-x%2B12 Combine like terms.


Now graph the equation y=-x%2B12 (note: let me know if you help graphing this)


graph%28500%2C500%2C-5%2C15%2C-8%2C12%2C-x%2B12%29 Graph of y=-x%2B12


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y=-abs%28x-10%29%2B2 Go back to the given equation


y=-%28-x%2B10%29%2B2 Replace abs%28x-10%29 with -x%2B10 (which is the second part)


y=x-10%2B2 Distribute the negative


y=x-8 Combine like terms.


Now graph the equation y=x-8


graph%28500%2C500%2C-5%2C15%2C-8%2C12%2Cx-8%29 Graph of y=x-8


Now graph the two equations together:


graph%28500%2C500%2C-5%2C15%2C-8%2C12%2C-x%2B12%2Cx-8%29 Graph of y=-x%2B12 (red) and graph of y=x-8 (green)

Because the sign in front of the absolute value is a negative sign, this tells us that we have to erase the portions of the graph that are above the intersection like this:


graph%28500%2C500%2C-5%2C15%2C-8%2C12%2C-abs%28x-10%29%2B2%29 Graph of y=-abs%28x-10%29%2B2


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Answer:

So the graph of y=-abs%28x-10%29%2B2 is

graph%28500%2C500%2C-5%2C15%2C-8%2C12%2C-abs%28x-10%29%2B2%29