document.write( "Question 1085663: Please may you help me solve:f(x)=|6-2x|+|X-1|-2X giving the necessary arguments before graphing.what is the range of the function?whenf(x)>0? \n" ); document.write( "

Algebra.Com's Answer #699735 by ikleyn(52790) $\"\"$ $\"About$

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document.write( "The critical points are 6-2x = 0, i.e. x = 3;  and x-1=0, i.e. x = 1.\r\n" );
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document.write( "If x < 1, then        6 - 2x > 0 and hence |6-2x} = (6-2x);\r\n" );
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document.write( "                      x - 1 < 0  and hence |x-1| = (1-x);\r\n" );
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document.write( "                      thus the entire function is f(x) = (6-2x) + (1-x) - 2x = 7 - 5x. \r\n" );
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document.write( "If 1 < x < 3,    then 6 - 2x > 0 and hence |6-2x} = (6-2x);\r\n" );
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document.write( "                      x - 1 > 0  and hence |x-1| = (x-1);\r\n" );
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document.write( "                      thus the entire function is f(x) = (6-2x) + (x-1) - 2x = 5 - 3x.\r\n" );
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document.write( "Lastly, if x > 3 then 6 - 2x < 0 and hence |6-2x} = (-6+2x);\r\n" );
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document.write( "                      x - 1 > 0  and hence |x-1| = (x-1);\r\n" );
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document.write( "                      thus the entire function is f(x) = (-6+2x) + (x-1) - 2x = -7 + x.\r\n" );
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document.write( "So you have the expressions for f(x) piecewise linear and can draw it like this\r\n" );
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document.write( "Plot y = |6-2x|+|X-1|-2X\r\n" );
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\n" ); document.write( "\n" ); document.write( "On plotting absolute value functions see the lessons\r
\n" ); document.write( "\n" ); document.write( "    How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 1 \r
\n" ); document.write( "\n" ); document.write( "    How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 2 \r
\n" ); document.write( "\n" ); document.write( "    How to plot functions containing Linear Terms under the Absolute Value sign. Lesson 3 \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
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\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this online textbook under the topic
\n" ); document.write( "\"Plotting Absolute values functions \".\r
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\n" ); document.write( "\n" ); document.write( "The strategy is to break up the entire set of real numbers into sub-domains (ranges) where the absolute value of linear term
\n" ); document.write( "is a linear function, and then to plot all these piece-wise linear functions.\r
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