SOLUTION: rewrite the equation y = -3|x -1| -3 as two linear functions f and g with restricted domains

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Question 1170688: rewrite the equation y = -3|x -1| -3 as two linear functions f and g with restricted domains
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39613)   (Show Source): You can put this solution on YOUR website!

Answer by ikleyn(52754)   (Show Source): You can put this solution on YOUR website!
.


We consider two cases.


Case 1.   Let x >= 1.


                 Then  x-1 >= 0;  hence,  |x-1| = x - 1;

                 then  y = f(x) = -3*(x-1) - 3 = - 3x + 3 - 3 = - 3x.




Case 2.   Let x < 1.


                 Then  x-1 <= 0;  hence,  |x-1| = -(x - 1);

                 then  y = g(x) = -3*(-(x-1)) - 3 = 3(x -1) - 3 = 3x - 6.



ANSWER.   If  x>=1,  then  y = f(x) = - 3x.

          If  x < 1, then  y = g(x) = 3x-6.

Solved, answered and explained.



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