Question

Find horizontal asymptotes of y = 2x / √(x² + 1):

A. y = 2
B. y = 1
C. y = -1
D. There are no horizontal asymptotes

Answer 1

The function y = 2x / √(x² + 1) has a horizontal asymptote at y = 2, as x approaches infinity or negative infinity. Hence, the correct answer is A. y = 2.

Step-by-step explanation:

To find the horizontal asymptotes of the function y = 2x / √(x² + 1), we need to determine the behavior of the function as x approaches infinity or negative infinity.

As x goes to infinity or negative infinity, the x² term dominates in the denominator, and the square root of x² behaves like x. Therefore, the function simplifies to:

y = 2x / x

Which further simplifies to:

y = 2

Thus, the function has a horizontal asymptote at y = 2.

The correct answer is A. y = 2.