Explain why the function F(x)= (4x^8+9)/(2x^4+11x^2+14) has no asymptotes and no intercept. Help....I really do need it.

Question

rational · Answer

vertical asymptotes occur when denominator becomes 0, 
is there any `x` value that makes the denominator become 0 ?

anonymous · Answer

no only if I were to use the quadratic formula it then would

rational · Answer

Notice that the denominator `(2x^4+11x^2+14) ` has all even powers, so its value is always positive no matter what the x is. so it never equals 0

rational · Answer

since denominator is never 0, the function will not have any vertical asymptotes

anonymous · Answer

wow I just noticed how simple this really is...Thank you for your help!