Question 200885
Just looking at it, you should be
able to answer a few questions.
(1) What is {{{g(x)}}} when {{{x=0}}}?
ans: {{{g(x)}}} is minus infinity
(2) What value of {{{x}}} makes {{{g(x)=0}}}?
ans:
{{{g(x)=3x-6/x+4}}}
{{{0 =3x-6/x+4}}}
{{{6/x = 3x + 4}}}
{{{6 = 3x^2 + 4x}}}
{{{3x^2 + 4x - 6 = 0}}}
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = 3}}}
{{{b = 4}}}
{{{c = -6}}}
{{{x = (-4 +- sqrt( 4^2-4*3*(-6) ))/(2*3) }}}
{{{x = (-4 +- sqrt( 16 + 72 ))/6 }}}
{{{x = (-4 +- sqrt(88))/6 }}}
{{{x = (-4 + 9.38)/6}}}
{{{x = 5.38/6}}}
{{{x = .897}}}
and
{{{x = (-4 - 9.38)/6}}}
{{{x = -13.38/6}}}
{{{x = -2.23}}}
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Now, I graph it
{{{ graph( 600, 600, -6, 6, -20, 20, 3x - 6/x + 4) }}}
My calculations look good