document.write( "Question 716457: What would the range and domain be for the function f(x)=(x+2)/(x^2-9)?
\n" ); document.write( "Also, for the range would you be able to say all real numbers since the function does cross over the horizontal asymptote? \n" ); document.write( "

Algebra.Com's Answer #439899 by KMST(5328) $\"\"$ $\"About$

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$\"f%28x%29=%28x%2B2%29%2F%28x%5E2-9%29\"$ has the graph $\"graph%28300%2C300%2C-10%2C10%2C-2%2C2%2C%28x%2B2%29%2F%28x%5E2-9%29%29\"$
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\n" ); document.write( "THE DOMAIN:
\n" ); document.write( "That function does not exist when $\"x%5E2-9=0\"$
\n" ); document.write( "because we cannot divide by zero.
\n" ); document.write( " $\"x%5E2-9=0\"$ happens when $\"x=3\"$ and when $\"x=-3\"$ .
\n" ); document.write( "Those two values of $\"x\"$ are not part of the domain.
\n" ); document.write( "Other than that,
\n" ); document.write( "the function works and gives a value of $\"f%28x%29\"$ to
\n" ); document.write( "every other real number $\"x\"$ .
\n" ); document.write( "NOTE:
\n" ); document.write( "You may be expected to use certain symbols and notation to state the domain.
\n" ); document.write( "Maybe you are expected to use set builder notation, such as
\n" ); document.write( "{real $\"x\"$ | $\"x%3C%3E3\"$ and $\"x%3C%3E-+3\"$ } or something like that.
\n" ); document.write( "Or maybe you are expected to use interval notation, as in
\n" ); document.write( "(infinite,-3)U(-3,3)U(3,infinite)
\n" ); document.write( "
\n" ); document.write( "THE RANGE:
\n" ); document.write( "The denominator has zeros at $\"x=-3\"$ and $\"x=3\"$ ,
\n" ); document.write( "but the numerator is not zero at those points,
\n" ); document.write( "so the function has vertical asymptotes at $\"x=-3\"$ and $\"x=3\"$ .
\n" ); document.write( "The function increases in absolute value without bounds as you approach $\"x=-3\"$ and $\"x=3\"$ .
\n" ); document.write( "It is negative on one side and positive on the other,
\n" ); document.write( "so it ranges from -infinity to infinity.
\n" ); document.write( "It does not just cross over the horizontal asymptote; it keeps going through all the real numbers, positive and negative
\n" ); document.write( "Its range is all the real numbers.
\n" ); document.write( " \n" ); document.write( "

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