document.write( "Question 211263This question is from textbook COLLEGE ALGEBRA
\n" ); document.write( ": Can you pls help me
\n" ); document.write( "3.)y=x^2-4x \r
\n" ); document.write( "\n" ); document.write( "•Graph this original function in its entire domain but coloring green that portion of the graph over the limited domain x>=2,\r
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\n" ); document.write( "\n" ); document.write( "•Find its inverse over x>=-4, \r
\n" ); document.write( "\n" ); document.write( "•On another set of coordinate axes, graph this inverse. Color it blue. On this same set of coordinate axis, graph the original f(x) on the limited domainx>= 2, y>=-4 & color it green.\r
\n" ); document.write( "\n" ); document.write( "•Draw the line y = x in dotted form.\r
\n" ); document.write( "\n" ); document.write( "•Label each graph including the dotted line by the corresponding equation and domain and range. Use the textbox for these labels.\r
\n" ); document.write( "\n" ); document.write( "Thanks alot for everybody who is willing to help.I dont know how to post a comment that's why I include this to my query \n" ); document.write( "

Algebra.Com's Answer #159628 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
First, let's graph $\"y=x%5E2-4x\"$ \r
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\n" ); document.write( "\n" ); document.write( "In order to graph $\"y=x%5E2-4x\"$ , we need to plot a few points.\r
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\n" ); document.write( "\n" ); document.write( "To get points in the form of (x,y), we need to find corresponding 'y' values to given 'x' values.\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-2\"$ note: you can start at any x value. \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-2%29%5E2-4%28-2%29\"$ Plug in $\"x=-2\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-4%28-2%29\"$ Square $\"-2\"$ to get $\"4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4--8\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=12\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-2\"$ , then $\"y=12\"$ which gives us the point (-2,12).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=-1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%28-1%29%5E2-4%28-1%29\"$ Plug in $\"x=-1\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-4%28-1%29\"$ Square $\"-1\"$ to get $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1--4\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=5\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=-1\"$ , then $\"y=5\"$ which gives us the point (-1,5).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%280%29%5E2-4%280%29\"$ Plug in $\"x=0\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0-4%280%29\"$ Square $\"0\"$ to get $\"0\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=0-0\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=0\"$ , then $\"y=0\"$ which gives us the point (0,0).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%281%29%5E2-4%281%29\"$ Plug in $\"x=1\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=1-4%281%29\"$ Square $\"1\"$ to get $\"1\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=1-4\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=-3\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=1\"$ , then $\"y=-3\"$ which gives us the point (1,-3).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=2\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%282%29%5E2-4%282%29\"$ Plug in $\"x=2\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=4-4%282%29\"$ Square $\"2\"$ to get $\"4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=4-8\"$ Multiply\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-4\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=2\"$ , then $\"y=-4\"$ which gives us the point (2,-4).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=3\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%283%29%5E2-4%283%29\"$ Plug in $\"x=3\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=9-4%283%29\"$ Square $\"3\"$ to get $\"9\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=9-12\"$ Multiply\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=-3\"$ Combine like terms.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=3\"$ , then $\"y=-3\"$ which gives us the point (3,-3).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=4\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%284%29%5E2-4%284%29\"$ Plug in $\"x=4\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=16-4%284%29\"$ Square $\"4\"$ to get $\"16\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=16-16\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=0\"$ Combine like terms.\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "So if $\"x=4\"$ , then $\"y=0\"$ which gives us the point (4,0).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=5\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%285%29%5E2-4%285%29\"$ Plug in $\"x=5\"$ .\r
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\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " $\"y=25-4%285%29\"$ Square $\"5\"$ to get $\"25\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=25-20\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=5\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=5\"$ , then $\"y=5\"$ which gives us the point (5,5).\r
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\n" ); document.write( "\n" ); document.write( "Let's find the y value when $\"x=6\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=%286%29%5E2-4%286%29\"$ Plug in $\"x=6\"$ .\r
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\n" ); document.write( "\n" ); document.write( " $\"y=36-4%286%29\"$ Square $\"6\"$ to get $\"36\"$ \r
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\n" ); document.write( "\n" ); document.write( " $\"y=36-24\"$ Multiply\r
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\n" ); document.write( "\n" ); document.write( " $\"y=12\"$ Combine like terms.\r
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\n" ); document.write( "\n" ); document.write( "So if $\"x=6\"$ , then $\"y=12\"$ which gives us the point (6,12).\r
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\n" ); document.write( "\n" ); document.write( "Now let's make a table of the values we just found.\r
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Table of Values:

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document.write( "x y
-2 12
-1 5
0 0
1 -3
2 -4
3 -3
4 0
5 5
6 12\r\n" );
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\r
\n" ); document.write( "\n" ); document.write( "Now let's plot the points:\r
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\r
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Graph:

\r
\n" ); document.write( "\n" ); document.write( "Now draw a curve through all of the points to graph $\"y=x%5E2-4x\"$ :\r
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Graph of $\"y=x%5E2-4x\"$ \r
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\n" ); document.write( "\n" ); document.write( "So the graph of $\"y=x%5E2-4x\"$ is\r
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\r
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\n" ); document.write( "\n" ); document.write( "Now shade the graph green from x=2 to the right like so:\r
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\r
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\n" ); document.write( "\n" ); document.write( "To find the inverse, we can do the following...\r
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\n" ); document.write( "\n" ); document.write( " $\"y=x%5E2-4x\"$ Start with the given equation.\r
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\n" ); document.write( "\n" ); document.write( " $\"x=y%5E2-4y\"$ Swap x and y\r
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\n" ); document.write( "\n" ); document.write( " $\"x=y%5E2-4y%2B4-4\"$ Take half of the y coefficient -4 to get -2. Square -2 to get 4. Add AND subtract this value on the right side.\r
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\n" ); document.write( "\n" ); document.write( " $\"x=%28y%5E2-4y%2B4%29-4\"$ Group the first three terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"x=%28y-2%29%5E2-4\"$ Factor that group\r
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\n" ); document.write( "\n" ); document.write( " $\"x%2B4=%28y-2%29%5E2\"$ Add 4 to both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"%28y-2%29%5E2=x%2B4\"$ Rearrange the terms.\r
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\n" ); document.write( "\n" ); document.write( " $\"y-2=%22%22%2B-sqrt%28x%2B4%29\"$ Take the square root of both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2B-sqrt%28x%2B4%29\"$ Add 2 to both sides.\r
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\n" ); document.write( "\n" ); document.write( " $\"y=2%2Bsqrt%28x%2B4%29\"$ or $\"y=2-sqrt%28x%2B4%29\"$ Break up the 'plus/minus'\r
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\n" ); document.write( "\n" ); document.write( "Now because the directions state that the graph has \"the limited domain x>=2\", this means that we're only going to focus on the positive portion of the inverse. So we're going to ignore $\"y=2-sqrt%28x%2B4%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "So the inverse of $\"y=x%5E2-4x\"$ (over the domain

) is $\"y=2%2Bsqrt%28x%2B4%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "I'll let you finish up and graph the inverse.\r
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