document.write( "Question 960716: How do I plot $\"f%28x%29+=+4x+-+3%2Fx\"$ ? Why doesn't the y-intercept 0,0 work in this case? \n" ); document.write( "

Algebra.Com's Answer #587115 by josgarithmetic(39623) $\"\"$ $\"About$

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f is undefined at x=0, because denominators must not become zero.\r
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\n" ); document.write( "\n" ); document.write( "You could make x y table of values, but you could also condense the function expression and evaluate a few things about it.\r
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\n" ); document.write( "\n" ); document.write( "First notice that as x goes unbounded to the left or the right, f(x) will approach 4x, so this will be a slant asymptote, of y=4x.\r
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\n" ); document.write( "\n" ); document.write( " $\"4x-3%2Fx\"$
\n" ); document.write( " $\"4x%28x%2Fx%29-3%2Fx\"$
\n" ); document.write( " $\"highlight%28%284x%5E2-3%29%2Fx%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "Where is the numerator 0?
\n" ); document.write( " $\"4x%5E2=3\"$
\n" ); document.write( " $\"x%5E2=3%2F4\"$
\n" ); document.write( " $\"x=3%2F2\"$ or $\"x=-3%2F2\"$ , so these are critical points, as is x=0.\r
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\n" ); document.write( "\n" ); document.write( "The three critical x values form intervals:
\n" ); document.write( " $\"-infin%3Cx%3C-3%2F2\"$
\n" ); document.write( " $\"-3%2F2%3Cx%3C0\"$
\n" ); document.write( " $\"0%3Cx%3C3%2F2\"$
\n" ); document.write( " $\"3%2F2%3Cx%3Cinfin\"$
\n" ); document.write( "Evaluate the sign of f in each interval. That will help to determine if f is above or below the horizontal axis.\r
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\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C4x-3%2Fx%29\"$ \r
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\n" ); document.write( "\n" ); document.write( "A vertical asymptote in addition to the slant asymptote, is x=0. \n" ); document.write( "

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