Question 1001253
A)


The smallest x allowed is x = -5 (from the first piece of the piecewise function)
There is no limit on the upper bound of x
So the domain in interval notation is <font color=red>[-5, infinity)</font>

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B)

Set each piece equal to 0 and solve for x


Piece 1:
x+6 = 0
x = -6
But x = -6 is outside of the domain. So this is not a proper intercept


Piece 2:
9 = 0 ... which is always false


Piece 3:
-x+4 = 0
-x = -4
x = 4


So the only x intercept is the ordered pair/point <font color=red>(4,0)</font>


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C)

To graph this piecewise function, you simply graph y = x+6, y = 9 and y = -x+4 but you apply the proper restrictions.


The graph of the piecewise function is shown below


<img src = "http://i.imgur.com/FwSJaJQ.png">


Notice how the red piece is the piece x+6 and it is only graphed from x = -5 to x = 1. There is a closed circle at x = -5 and an open circle at x = 1. The closed circle means "include this point" while the open circle means "exclude this point"


There is a single solitary point at (1,9). This represents the middle piece "f(x) = 9 if x = 1"


Finally, the last piece is -x+4 and is it the piece in green. It has an open circle at the endpoint and stretches on forever the more x increases.