Question

1. identify the horizontal asymptotes $f(x) = \frac{x + 4}{x^2 + 5x + 4}$ teks a2.6(k)\

a) $y = 0$\
b) no horizontal asymptote\
c) $y = 1$\
d) $y = -4$

Explanation:

Step1: Analyze the degrees of numerator and denominator

The function is \( f(x)=\frac{x + 4}{x^{2}+5x + 4} \). The degree of the numerator (highest power of \( x \)) is \( 1 \) (from \( x \)), and the degree of the denominator is \( 2 \) (from \( x^{2} \)).

Step2: Apply the rule for horizontal asymptotes

For a rational function \( \frac{N(x)}{D(x)} \), if the degree of \( N(x) \) (let's say \( n \)) is less than the degree of \( D(x) \) (let's say \( m \)), then the horizontal asymptote is \( y = 0 \). Here, \( n=1 \) and \( m = 2 \), so \( n

Answer:

A) \( y = 0 \)