SOLUTION: Determine the domain and the range of the function g(x)=(4x-4)/(5x-30).

Algebra ->  Functions -> SOLUTION: Determine the domain and the range of the function g(x)=(4x-4)/(5x-30).      Log On


   

Question 347663: Determine the domain and the range of the function g(x)=(4x-4)/(5x-30).
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!

g%28x%29=%284x-4%29%2F%285x-30%29

The domain is all x except those that make the denominator zero (shown in blue below).
Domain:(-infinity,6) U (6,infinity)
.
.
.
The range is all values except the asymptote value (shown in green below),
g%28x%29=%284%2F5%29%28%28x-1%29%2F%28x-6%29%29
g%28x%29=%284%2F5%29%28%281-1%2Fx%29%2F%281-6%2Fx%29%29
As x becomes infintely large, g(x) becomes,
g%28x%29=%284%2F5%29%28%281-0%29%2F%281-0%29%29
g%28x%29=4%2F5
Range:(-infinity,4%2F5) U (4%2F5,infinity)
.
.