First of all, what is a rational function?
Secondly, how do I find the domain of rational functions?
Find the domain of each rational function below.
[1] Q(x) = -x(1 - x)/(3x^2 +5x -2)
[2] F(x) = -2(x^2 - 4)/3(x^2 + 4x + 4)
A rational function is a function of a quotient (fraction) of two polynomial functions.
The "bad" points are where the denominator is zero.Secondly, how do I find the domain of rational functions?
Again the denominator is not zero.Find the domain of each rational function below.
[1] Q(x) = -x(1 - x)/(3x^2 +5x -2)
Thus,
$\displaystyle 3x^2+5x-2=0$
Find those $\displaystyle x$.
And then the domain is all $\displaystyle x$ EXCEPT the ones you found just above.
Same approach to other problem.