document.write( "Question 529116: $\"+%282x+-+6%29+%2F+%28x%5E2%2B3x-10%29+\"$
\n" ); document.write( "What I have to do here is find the y-intercept, the zeros, domain, x-intercept, and end behavior. \r
\n" ); document.write( "\n" ); document.write( "I know that you have to simplify the factors, which would be
\n" ); document.write( " $\"+2%28x-3%29+%2F+%28x%2B5%29+%28x-2%29+\"$
\n" ); document.write( "I just don't know what else to do to find the rest. I know that to find the y-intercept you have to set the x to zero, correct? And to find the x-intercept you set the whole equation to zero. \n" ); document.write( "

Algebra.Com's Answer #349511 by KMST(5328) $\"\"$ $\"About$

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\n" ); document.write( "You are correct about the y-intercept.
\n" ); document.write( "The factoring
\n" ); document.write( " $\"y=%282%28x-3%29%29%2F%28%28x%2B5%29%28x-2%29%29\"$
\n" ); document.write( "tells you a lot about the function.
\n" ); document.write( "Look at when each factor in parenthesis is zero.
\n" ); document.write( "It says that for $\"x=3\"$ $\"y=0\"$ .
\n" ); document.write( "That's the x intercept, where the graph crosses the x-axis.
\n" ); document.write( "You also see from the factoring that the function changes sign each time one of those parentheses changes sign.
\n" ); document.write( "It is negative when all three parentheses are negative, for $\"x%3C-5\"$ .
\n" ); document.write( "It becomes positive between -5 and 2.
\n" ); document.write( "It's negative again between 2 and 3,
\n" ); document.write( "and it's positive for $\"x%3E3\"$ .
\n" ); document.write( "You also see that the function does not exist for
\n" ); document.write( " $\"x=-5\"$ and for $\"x=2\"$
\n" ); document.write( "because they make the denominator zero. Those values of x are not part of the domain of the function, but other than that, all other real numbers are in the domain.
\n" ); document.write( "As x approaches -5, the factor $\"%28x%2B5%29\"$ aproaches zero, while the other factors are close to finite numbers. Very near -5, the function could be approximated by
\n" ); document.write( " $\"%282%28-5-3%29%29%2F%28%28x%2B5%29%28-5-2%29%29=%2816%2F7%29%281%2F%28x%2B5%29%29\"$ .
\n" ); document.write( "That means it goes down towards minus infinity on the left side of the vertical line x=5 and comes back down from plus infinity on the other side of -5.
\n" ); document.write( "Something similar, but reversed happens around x=2.
\n" ); document.write( "Both, x=-5 and x=2 are vertical asymptotes.
\n" ); document.write( "Even more can be said about the behavior of the function.
\n" ); document.write( "For very large x, and for very large -x, y is very small. The function hugs the x- axis as you go to one or the other extremes of x. The x- axis is an asymptote on both sides (a horizontal one).
\n" ); document.write( "Maybe you could see that better if you wrote it as
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