SOLUTION: State the domain of r(x) and range of r(x) in the equation r(x)=(6x+12)/(x^2-16)

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Question 2392: State the domain of r(x) and range of r(x) in the equation r(x)=(6x+12)/(x^2-16)
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
re-arrange this to simplify it, so you can see the equation better...
r(x) = %286%28x%2B2%29%29%2F%28%28x%2B4%29%28x-4%29%29
now for these "fractional equations, you need to do some investigations as to its shape...first, the denominator will freak out when x is either +4 or -4, so these 2 values are NOT allowed..they are asymptotes....the curve gets closer to it but never reaches it.
so we have a graph in 3 parts...before x=-4, greater than x=4 and the region between.
now, if x is HUGE and -ve...eg -1000000, what will y be heading towards?...infinity? -infinity? or zero?..answer...towards zero from a negative side.
Now, if x is HUGE and +ve, eg 1000000, y will again head for zero but from a +ve side.
In between, if x=0, then y is just negative...this is an elongated S-shape...try it and sketch it...

Basically: domain is any value except +4 or -4
range is any value of y is possible.
jon