Question 972886
Consider the function {{{ (3x^2-2x-4)/(x+2) }}}
a)  Find the equation of the slant asymptote algebraically.
b)  Using a graphing calculator, find the range of f(x).  Explain the process you used.
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Perform long division:

.................3x........-8.................
..x+2..|.....3x^2.....-2x.......-4........
................3x^2.....6x....................
............................-8x.......-4........
............................-8x.......-16.....
.........................................12....
{{{ (3x^2-2x-4)/(x+2)=(3x-8)+(12/(x+2))}}}
Equation of slant asymptote=3x-8 (Ignore remainder)
Using a graphic calculator: 
Range: (-2, ∞)
see graph below:
{{{ graph( 300, 300, -10, 10, -10, 10, (3x^2-2x-4)/(x+2),(3x-8)) }}}