Let f ( x ) =(2x^2+7x+5)/(3x^2+20x+25) .Consider the end behavior and the behavior at each asymptote.

Question

As x → ∞, y→ _____

As x → −∞, y→ _____

As x → −5^-,y→ _____

As x → −5^+,y→ _____

As x → −5/3^−,y→ _____

As x → −5/3^+,y→ _____

Answer 1

To look at end behavior you just need to consider the ration of the highest order term which is 2/3 so as x approaches either positive or negative infinity y will approach 2/3

asymptotes will occur wherever the denominator is zero. To find this factor the denominator into

(3x+5)(x+5)=0 x=-3/5 and x=-5