Question

find all horizontal asymptotes of the following function.
$f(x) = \frac{3(x + 4)(x - 4)}{2x(x + 4)}$
answer attempt 1 out of 2
one horizontal asymptote

Explanation:

Step1: Simplify the function

Cancel common factor $(x + 4)$: $f(x) = \frac{3(x - 4)}{2x}$ (for $x
eq -4$)

Step2: Find leading terms

Numerator: $3x - 12$, leading term $3x$; Denominator: $2x$, leading term $2x$

Step3: Compute limit at infinity

$\lim_{x \to \infty} \frac{3x}{2x} = \frac{3}{2}$

Step4: Confirm horizontal asymptote

Horizontal asymptote is $y = \frac{3}{2}$

Answer:

$\frac{3}{2}$