Question 347663

{{{g(x)=(4x-4)/(5x-30)}}}
{{{g(x)=(4(x-1))/(5(x-6))
{{{g(x)=(4/5)((x-1)/(x-6))}}}
The domain is all x except those that make the denominator zero (shown in blue below).
Domain:({{{-infinity}}},{{{6}}}) U ({{{6}}},{{{infinity}}})
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The range is all values except the asymptote value (shown in green below),
{{{g(x)=(4/5)((x-1)/(x-6))}}}
{{{g(x)=(4/5)((1-1/x)/(1-6/x))}}}
As x becomes infintely large, g(x) becomes,
{{{g(x)=(4/5)((1-0)/(1-0))}}}
{{{g(x)=4/5}}}
Range:({{{-infinity}}},{{{4/5}}}) U ({{{4/5}}},{{{infinity}}})

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{{{drawing(300,300,-8,12,-10,10,blue(line(6,-100,6,100)),green(line(-100,4/5,100,4/5)),graph(300,300,-8,12,-10,10,(4x-4)/(5x-30)))}}}