Step-by-step explanation:
To find the asymptote of the function \( A(x) = \frac{2}{x} - 1 \), we need to determine the values of \( x \) for which the function approaches infinity or negative infinity.
The function \( A(x) \) has a vertical asymptote wherever the denominator becomes zero, because division by zero is undefined. In this case, the denominator \( x \) becomes zero when \( x = 0 \). Therefore, \( x = 0 \) is a vertical asymptote.
The horizontal asymptote of the function can be found by examining the behavior of the function as \( x \) approaches positive or negative infinity. As \( x \) becomes very large in magnitude (either positively or negatively), the term \( \frac{2}{x} \) becomes very small, approaching zero. Therefore, the horizontal asymptote is the line \( y = -1 \).
So, the asymptotes of the function \( A(x) = \frac{2}{x} - 1 \) are:
- Vertical asymptote: \( x = 0 \)
- Horizontal asymptote: \( y = -1 \)
