(A) find the domain of the function, (B) decide if the function is continuous, and (c) identify your horizontal and vertical asymptotes.

F(x)= (3x^2+1)/(x^2+x+9)

Find the zeros (if any) of the rational function.
G(x)= (x^3-8)/x^2+4
H(x)=5 + 3/(x^2+1)
G(x)= (x^2-5x+6)/(x^2+4)
These are the last questions or problems I have on my homework and I don't know how to do them. Please show and tell me how to do them!

1 answer

(A)
The denominator never zero, so the domain is all real numbers. So, of course F(x) is continuous, since there are no places where it is undefined. As x gets large, F(x) ≈ 3x^2/x^2 = 3.

For the zeros of rational functions, they occur where the numerator is zero (as long as the denominator is not also zero).