Final answer:
The limit of f(x) as x approaches infinity is 1, indicating a horizontal asymptote at y = 1, with no slant asymptote present.
Step-by-step explanation:
The limit of the function f(x) as x approaches infinity, given by f(x) = 1 - e-2x, is 1. The term e-2x approaches zero as x approaches infinity, resulting in the remaining constant value of 1. This suggests the function has a horizontal asymptote at y = 1. As there is no term in f(x) that grows without bound in the form of x times a function of x (which would suggest a slant asymptote), the horizontal asymptote fully describes the behavior of f(x) as x tends toward infinity.
To evaluate the limit of f(x) as x approaches infinity, we can look at the behavior of the function as x gets larger and larger.
For the function f(x) = 1 - e^(-2x), as x approaches infinity, the exponential term e^(-2x) approaches 0. Therefore, the limit of f(x) as x approaches infinity is 1 - 0, which is equal to 1.
There are no horizontal or slant asymptotes for this function.