document.write( "Question 687244: For the function g(x) = 1/x-4 + 2:
\n" ); document.write( "Write the equations of the asymptotes and label them on the coordinate plane.
\n" ); document.write( "Enter at least five values in the table of values.
\n" ); document.write( "Graph the function on the coordinate plane.
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Algebra.Com's Answer #425130 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
I believe you mean g(x) = 1/(x-4) + 2,
\n" ); document.write( "which I can write as
\n" ); document.write( " $\"g%28x%29=1%2F%28x-4%29%2B2\"$ .
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\n" ); document.write( "The function $\"f%28x%29=1%2Fx\"$ $\"graph%28200%2C200%2C-8%2C8%2C-8%2C8%2C1%2Fx%29\"$ is sort of an ancestor of your function.
\n" ); document.write( "It has the x- and y-axes for asymptotes.
\n" ); document.write( "The y-axis, $\"x=0\"$ is a vertical asymptote
\n" ); document.write( "because the function does not exist for $\"x=0\"$ (it is not continuous at $\"x=0\"$ )
\n" ); document.write( "but as you approach $\"x=0\"$ , from either side,
\n" ); document.write( " $\"abs%28f%28x%29%29=abs%281%2Fx%29\"$ grows without bounds.
\n" ); document.write( "The horizontal x-axis, $\"y=0\"$ , is an asymptote because as $\"abs%28x%29\"$ grows larger (at both ends of the x-axis),
\n" ); document.write( " $\"f%28x%29=1%2Fx\"$ approaches zero.
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\n" ); document.write( "The function $\"h%28x%29=1%2F%28x-4%29\"$ $\"graph%28200%2C200%2C-6%2C10%2C-8%2C8%2C1%2F%28x-4%29%29\"$
\n" ); document.write( "is the same, but moved 4 units to the right, a closer ancestor.
\n" ); document.write( "Its asymptotes are $\"x=4%7D%7D+and+%7B%7B%7By=0\"$ .
\n" ); document.write( " $\"x=4\"$ (vertical asymptote, where the function is not continuous), and
\n" ); document.write( " $\"y=0\"$ (again).
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\n" ); document.write( "Adding $\"2\"$ to that function gives you $\"g%28x%29=1%2F%28x-4%29%2B2\"$ .
\n" ); document.write( "The graph is $\"graph%28200%2C200%2C-6%2C10%2C-4%2C12%2C1%2F%28x-4%29%2B2%2C2%29\"$
\n" ); document.write( "and the asymptotes are $\"y=2\"$ and
\n" ); document.write( " $\"x=4\"$ .
\n" ); document.write( "
\n" ); document.write( "Just five points seems too little for this function, but the symmetry might help.
\n" ); document.write( "For $\"x=4.1\"$ , $\"g%28x%29=1%2F%284.1-4%29%2B2=1%2F0.1%2B2=10%2B2=12\"$ .
\n" ); document.write( "(Symmetrically, for $\"x=3.9\"$ , $\"g%28x%29=1%2F%283.9-4%29%2B2=1%2F%28-0.1%29%2B2=-10%2B2=-8\"$ .
\n" ); document.write( "For $\"x=4.5\"$ , $\"g%28x%29=1%2F%284.5-4%29%2B2=1%2F0.5%2B2=2%2B2=4\"$ .
\n" ); document.write( "(Symmetrically, for $\"x=3.5\"$ , $\"g%28x%29=1%2F%283.5-4%29%2B2=1%2F%28-0.5%29%2B2=-2%2B2=0\"$ .
\n" ); document.write( "For $\"x=5\"$ , $\"g%28x%29=1%2F%285-4%29%2B2=1%2F1%2B2=1%2B2=3\"$ .
\n" ); document.write( "(Symmetrically, for $\"x=3\"$ , $\"g%28x%29=1%2F%283-4%29%2B2=1%2F%28-1%29%2B2=-1%2B2=1\"$ .
\n" ); document.write( "For $\"x=9\"$ , $\"g%28x%29=1%2F%289-4%29%2B2=1%2F5%2B2=0.2%2B2=2.2\"$ .
\n" ); document.write( "(Symmetrically, for $\"x=-1\"$ , $\"g%28x%29=1%2F%28-1-4%29%2B2=1%2F%28-5%29%2B2=-0.2%2B2=1.8\"$ .
\n" ); document.write( "For $\"x=14\"$ , $\"g%28x%29=1%2F%2814-4%29%2B2=1%2F10%2B2=0.1%2B2=2.1\"$ .
\n" ); document.write( "(Symmetrically, for $\"x=-6\"$ , $\"g%28x%29=1%2F%28-6-4%29%2B2=1%2F%28-10%29%2B2=-0.1%2B2=1.9\"$ .
\n" ); document.write( "We can plot those points as blue dots and connect them.

\n" ); document.write( "We can draw the asymptotes in green too. \n" ); document.write( "

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