SOLUTION: sketch the graph of y=f(x)=|6-2x|+|x-1|-2x , what is the range of the function ? when is f(x)>0 ?

Algebra ->  Graphs -> SOLUTION: sketch the graph of y=f(x)=|6-2x|+|x-1|-2x , what is the range of the function ? when is f(x)>0 ?      Log On


   

Question 1084538: sketch the graph of y=f(x)=|6-2x|+|x-1|-2x ,
what is the range of the function ? when is f(x)>0 ?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=f%28x%29=abs%286-2x%29%2Babs%28x-1%29-2x
graph: just do several points and draw a graph that looks like this

+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2Cabs%286-2x%29%2Babs%28x-1%29-2x%29+

the range of the function:
{ y element R : y%3E=-4 }

when is f%28x%29%3E0+?
first find zeros:
0+=+-2x+%2B+sqrt%28%28-2%28x-3%29%5E2%29%29+%2B+sqrt%28%28x+-1%29%5E2%29

0=-2x+%2B+-2%28x-+3%29+%2B+%28x+-+1%29
2x+=++-+2x%2B6%2B+x+-+1
2x+=+5+-+x
2x%2Bx+=+5
3x+=+5
x+=+5%2F3
0=-2x+-%28-2%28x+-+3%29%29+%2B%28x+-+1%29
0=-2x+%2B2%28x+-+3%29%29+%2Bx+-+1
0=-2x+%2B2x+-+6+%2Bx+-1
0=+-+7+%2Bx+
x+=+7

so, f%28x%29%3E0+ from -infinity to +5%2F3 and from 7 to +infinity