document.write( "Question 153933: what does this look like plotted out on a graph? I want to grasp the knowledge but need to see it in front of me as an example. Thank you for your help.\r
\n" ); document.write( "\n" ); document.write( "y = |x| + 3 \n" ); document.write( "

Algebra.Com's Answer #113316 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Actually, the best way to understand it is not by staring
\n" ); document.write( "at a graph (you can do that later). The best way is just
\n" ); document.write( "to reason out what it should look like.
\n" ); document.write( "I'll do it in steps:
\n" ); document.write( "(1) The right side (therefore $\"y\"$ ) can never be negative
\n" ); document.write( "because neither of the two terms on the right can ever be negative.
\n" ); document.write( " $\"abs%28x%29\"$ means \"make the sign of $\"x\"$ positive,
\n" ); document.write( "no matter what $\"x\"$ is.
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) The right side can be equal to $\"3\"$ , but it can never
\n" ); document.write( "be less that $\"3\"$ , since $\"abs%28x%29\"$ will never subtract
\n" ); document.write( "anything from it
\n" ); document.write( "--------------------------
\n" ); document.write( "(3) I can get rid of the absolute value sign if I replace
\n" ); document.write( "the equation with 2 equations like this:
\n" ); document.write( "When $\"x\"$ is zero or negative the equation is
\n" ); document.write( " $\"y+=+-x+%2B+3\"$
\n" ); document.write( "When $\"x\"$ is zero or positive the equation is
\n" ); document.write( " $\"y+=+x+%2B+3\"$
\n" ); document.write( "Suppose $\"x+=+-5\"$ , then
\n" ); document.write( " $\"y+=+-%28-5%29+%2B+3\"$
\n" ); document.write( " $\"y+=+8\"$
\n" ); document.write( "This shows that $\"y\"$ is positive for + $\"x\"$
\n" ); document.write( "and - $\"x\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "(4) Using the reasoning of these steps, $\"y+%3E=+3\"$
\n" ); document.write( " $\"x\"$ can be any value (there are no restrictions on
\n" ); document.write( "what you make it).
\n" ); document.write( "(5) To draw the graph, draw $\"y+=+-x+%2B+3\"$ , but don't let
\n" ); document.write( "the line go below $\"y+=+3\"$ , then draw $\"y+=+x+%2B+3\"$
\n" ); document.write( "and don't let the line go below $\"y+=+3\"$
\n" ); document.write( "----------------------------
\n" ); document.write( "Hope that's not too confusing. There no easy way except to
\n" ); document.write( "apply a step-by-step reasoning that makes sense to you. \n" ); document.write( "

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