Which statement is true regarding horizontal asymptotes?

The graph will trend toward the horizontal asymptote but never touch it.

Two of these are correct.

None of these are correct.

Exponential functions have an asymptote represented by the line y=0.

1 answer

The correct statement regarding horizontal asymptotes is:

Two of these are correct.

Here's the reasoning:

  1. The graph will trend toward the horizontal asymptote but never touch it. - This statement is generally true for many functions that have horizontal asymptotes, particularly rational functions.

  2. Exponential functions have an asymptote represented by the line y=0. - This is also true for certain exponential functions, particularly those that approach zero (e.g., \(y = e^{-x}\) as \(x \to \infty\)).

Given that both of the first two options are correct, the statement "Two of these are correct" is the most accurate choice.