document.write( "Question 936735: 1) can you graph: f(x)= abs(2x-5) for 0<=x<=5
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Algebra.Com's Answer #572672 by Edwin McCravy(20056) $\"\"$ $\"About$

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$\"matrix%281%2C5%2C++%22f%28x%29%22%2C%22%22=%22%22%2Cabs%282x-5%29%2C+for%2C+0%3C=x%3C=5%29\"$ \r
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document.write( "To find the x-coordinate of the vertex, (the sharp point),\r\n" );
document.write( "we set what's between the bars | | equal to 0. What's\r\n" );
document.write( "between the bars is 2x-5, so we set that = 0\r\n" );
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document.write( "          2x-5 = 0\r\n" );
document.write( "            2x = 5\r\n" );
document.write( "             x = 2.5\r\n" );
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document.write( "To find the y-coordinate of the vertex (sharp point) we \r\n" );
document.write( "substitute that in the equation:\r\n" );
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document.write( "So the vertex is (2.5,0)\r\n" );
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document.write( "Get two more points one on each side of the vertex,\r\n" );
document.write( "May as well pick the endpoints of the domain  \r\n" );
document.write( " using x = 0 on the left and x = 5\r\n" );
document.write( "on the right:\r\n" );
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document.write( "That's the point (0,5)\r\n" );
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document.write( "That's the point (5,5)\r\n" );
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document.write( "So we plot the vertex (2.5,0), and endpoints (0,0) and (5,5)\r\n" );
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document.write( "The graph stops at (0,0) on the left and at (5,5) on the right\r\n" );
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document.write( "Since f(x) includes both endpoints, we draw a darkened circle\r\n" );
document.write( "at each endpoint:\r\n" );
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document.write( "---------\r\n" );
document.write( "f(x)= {x if x<=0 \r\n" );
document.write( "x+1 if x>0\r\n" );
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document.write( "Get a couple of points on the part where f(x) = y = x, say \r\n" );
document.write( "(-2,-2) and (-4,-4) and the endpoint (0,0)\r\n" );
document.write( "and draw the line but stop it at 0 and draw a darkened circle to show\r\n" );
document.write( "that it includes that since the \"if\" part is \r\n" );
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document.write( "But thats only half the graph.\r\n" );
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document.write( "Get a couple of points on the part where f(x) = y = x+1, say \r\n" );
document.write( "(1,2) and (2,3).  The right part of the graph will not include\r\n" );
document.write( "the endpoint since the \"if\" part is . However, we find \r\n" );
document.write( "what the endpoint would have been if it had been included\r\n" );
document.write( "anyway, and draw an open circle there to indicate that it is \r\n" );
document.write( "not included.\r\n" );
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document.write( "If the right part had included the endpoint where x=0, it would have \r\n" );
document.write( "been at y=1+1 or y=2. So we draw an open circle at (0,2) and continue\r\n" );
document.write( "the line to the right.  Here is the final graph. \r\n" );
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document.write( "Edwin

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