Question 2392
re-arrange this to simplify it, so you can see the equation better...

r(x) = {{{(6(x+2))/((x+4)(x-4))}}}

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