document.write( "Question 619997: How can I graph this rational function by combining all terms over a common denominator: R(x)=2/3 + 28/3x + 16/x^2 \n" ); document.write( "
Algebra.Com's Answer #389877 by lwsshak3(11628)\"\" \"About 
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How can I graph this rational function by combining all terms over a common denominator:
\n" ); document.write( "R(x)=2/3 + 28/3x + 16/x^2
\n" ); document.write( "LCD: 3x^2
\n" ); document.write( "R(x)=(2x^2 + 28x + 48)/3x^2
\n" ); document.write( "=(2x+4)(x+12)/3x^2
\n" ); document.write( "Horizontal asymptote: 2/3 (divide lead coefficient of numerator by lead coefficient of denominator.
\n" ); document.write( "Vertical asymptote: set denominator=0, then solve for x.
\n" ); document.write( "3x^2=0
\n" ); document.write( "x=0 (vertical asymptote)
\n" ); document.write( "..
\n" ); document.write( "x-intercepts: set y=0, then solve for x
\n" ); document.write( "(2x+4)(x+12)=0
\n" ); document.write( "2x+4=0
\n" ); document.write( "2x=-4
\n" ); document.write( "x=-2
\n" ); document.write( "and
\n" ); document.write( "x+12=0
\n" ); document.write( "x=-12
\n" ); document.write( "x-intercepts at -2 and -12
\n" ); document.write( "..
\n" ); document.write( "y-intercept: set x=0, then solve for y
\n" ); document.write( "y=48/0= undefined
\n" ); document.write( "y-intercept: none
\n" ); document.write( "..
\n" ); document.write( "number line:\r
\n" ); document.write( "\n" ); document.write( "<...+....-12...-....-2....+.....0.....+......>\r
\n" ); document.write( "\n" ); document.write( "see graph below as a visual check
\n" ); document.write( " \"+graph%28+300%2C+300%2C+-10%2C+10%2C+-10%2C+10%2C%282x%5E2+%2B+28x+%2B+48%29%2F3x%5E2%29+\"\r
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