Question

find all horizontal asymptotes of the following function
$f(x) = \frac{15x - 9}{5x + 9}$
answer attempt 1 out of 3
no horizontal asymptotes
one horizontal asymptote
two horizontal asymptotes
$y = 3$
submit answer

Explanation:

Step1: Recall Horizontal Asymptote Rule

For a rational function \( f(x)=\frac{ax^n + \dots}{bx^m + \dots} \), if \( n = m \), the horizontal asymptote is \( y=\frac{a}{b} \).
Here, \( f(x)=\frac{15x - 9}{5x + 9} \), degree of numerator (\( n \)) and denominator (\( m \)) is 1 (so \( n = m \)).

Step2: Apply the Rule

The leading coefficients are \( a = 15 \) (from numerator) and \( b = 5 \) (from denominator). So horizontal asymptote is \( y=\frac{15}{5}=3 \). Also, since \( n = m \), there is one horizontal asymptote.

Answer:

One Horizontal Asymptote, \( y = 3 \)