SOLUTION: I don't have a graphing calculator can you show without a calculator the rational function g(x)=3x-6/x+4? please show me how to do this problem.

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Question 200885: I don't have a graphing calculator can you show without a calculator the rational function g(x)=3x-6/x+4? please show me how to do this problem.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Just looking at it, you should be
able to answer a few questions.
(1) What is g%28x%29 when x=0?
ans: g%28x%29 is minus infinity
(2) What value of x makes g%28x%29=0?
ans:
g%28x%29=3x-6%2Fx%2B4
0+=3x-6%2Fx%2B4
6%2Fx+=+3x+%2B+4
6+=+3x%5E2+%2B+4x
3x%5E2+%2B+4x+-+6+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+3
b+=+4
c+=+-6
x+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A3%2A%28-6%29+%29%29%2F%282%2A3%29+
x+=+%28-4+%2B-+sqrt%28+16+%2B+72+%29%29%2F6+
x+=+%28-4+%2B-+sqrt%2888%29%29%2F6+
x+=+%28-4+%2B+9.38%29%2F6
x+=+5.38%2F6
x+=+.897
and
x+=+%28-4+-+9.38%29%2F6
x+=+-13.38%2F6
x+=+-2.23
-----------------------
Now, I graph it
+graph%28+600%2C+600%2C+-6%2C+6%2C+-20%2C+20%2C+3x+-+6%2Fx+%2B+4%29+
My calculations look good