Need to check my horitontal asymptotes question

Question

Please show me how to do it also. Also when I am doing this question, I only look at the biggest exponent when applying my rule right? I don't care about the number before the x, just the highest exponent. Well what if the top has x^2 and bot have no x? or what if x^3/x?

Answer 1

(8).

The function is f(x) = 1 / (x² - 8x + 15).

In the above function, numerator function [N(x) = 1] and denominator function [D(x) = x² - 8x + 15] have no common factors.

The graph of f(x) function has one or no horizontal asymptote determined by comparing the degrees of numerator function and denominator function.

Degree of numerator function( = 0) < Degree of denominator function( = 2).

Therefore, horizontal asymptote is y = 0( the x-axis).

The horizontal asymptote y = 0.

Answer 2

(9).

The function is f(x) = (3x² - 100) / (x² + 1000).

In the above function, numerator function [N(x) = 3x² - 100] and denominator function [D(x) = x² + 1000] have no common factors.

The graph of f(x) function has one or no horizontal asymptote determined by comparing the degrees of numerator function and denominator function.

Degree of numerator function = 2 = Degree of denominator function.

Therefore, horizontal asymptote is y = a_n/b_n = leading coefficient of numerator function / leading coefficient of denominator function = 3/1 = 3.

The horizontal asymptote y = 3.