Which function has a horizontal asymptote at y = 3?

Question

asked Jul 27, 2024 133k views

1 Answer

Danielle Madeley · Answer 1 · 2024-07-31T22:49:10+0000

Answer: A)
f(x)=(6x^2-x+4)/(2x^2-1)

Explanation:

Line
y=L is a horizontal asymptote of the function
y=f(x) , if either
$\lim_(x \to \infty) f(x)=L$ or
$\lim_(x \to \infty) f(x)=L$ , and
is finite.

calculate the limits:

$\lim_(x \to \infty) ((6x^2-x+4)/(2x^2-1))=3$

$\lim_(x \to -\infty) ((6x^2-x+4)/(2x^2-1))=3$

Thus, the horizontal asymptote is
y=3