SOLUTION: This question is really bothering me. Please help. Express f(x) = x2 + │x+3│ - 1 without the absolute values and hand-graph. Hint: &#9

Algebra ->  Rational-functions -> SOLUTION: This question is really bothering me. Please help. Express f(x) = x2 + │x+3│ - 1 without the absolute values and hand-graph. Hint: &#9      Log On


   

Question 86978: This question is really bothering me. Please help. Express f(x) = x2 + │x+3│ - 1 without the absolute values and hand-graph.
Hint: │x│= x if x ≥ 0 or
= –x if x < 0
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Express f(x) = x^2 + │x+3│ - 1 without the absolute values and hand-graph.
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Note:
|x+3| = x+3 if x+3>=0; that is x>=-3
|x+3| = -(x+3) if x+3 <0; that is x<-3
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So, for x<-3 your equation becomes:
f(x) = x^2 -x-3-1
f(x) = x^2-x-4
Graph this parabola to the left of x=-3.
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And for x>=-3 you equation becomes:
f(x) = x^2+x+3-1
f(x) = x^2+x+2
Graph this parabola at and to the right of x=-3
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Cheers,
Stan H.
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