document.write( "Question 729979: i have to graph an open sentence its for absolute value. i know that if i have /x/=3 this is is x=3 or x=-3 but how do i graph y=2/x+4/ its y=2x+4 or ??? \n" ); document.write( "

Algebra.Com's Answer #446307 by josgarithmetic(39620) $\"\"$ $\"About$

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The variable expression, x+4, may be either positive or negative, depending on the value of x. \r
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\n" ); document.write( "\n" ); document.write( "When $\"x%2B4%3E=0\"$ , $\"y=2abs%28x%2B4%29\"$ is $\"y=2%28x%2B4%29\"$ or $\"y=2x%2B8\"$ . You must restrict the graph of this line to satisfy $\"x%2B4%3E0\"$ which is $\"x%3E=-4\"$ . \r
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\n" ); document.write( "\n" ); document.write( "When $\"x%2B4%3C0\"$ , $\"y=2abs%28x%2B4%29\"$ is $\"y=2%2A%28-1%29%28x%2B4%29\"$ , or $\"y=2%28-x-4%29\"$ , or $\"y=-2x-8\"$ . You must restrict the graph of this line to satisfy $\"x%2B4%3C0\"$ which is $\"x%3C-4\"$ . \r
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\n" ); document.write( "\n" ); document.write( "IN CASE OF CONTINUED DIFFICULTY:
\n" ); document.write( "The absolute value of an expression requires simple but careful attention to logic. |x+4| will always be positive or zero. NEVER Negative.
\n" ); document.write( "If x+4=0>0, then |x+4|=x+4.
\n" ); document.write( "If x+4<0, then |x+4|=-(x+4)=-x-4.
\n" ); document.write( "Really that is based on the meaning of absolute value.
\n" ); document.write( "For any variable, v, we can consider how far is v from zero on the number line. |v| is the distance from zero on the number line. v is a variable, so by itself, we do not know its value; but |v| is equal to v if $\"v%3E=0\"$ , and |v| is equal to -v if $\"v%3C0\"$ .
\n" ); document.write( "Drawing a number line makes this easier to SEE. \n" ); document.write( "

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