The function h(x)=(x^2-1)/(x^2)+1 has the following asymptotes. (You can choose more than one). a) Vertical asymptote b) Horizontal asymptote c) Oblique asymptote

## Step 1: Finding Vertical Asymptotes<br />### Vertical asymptotes occur when the denominator of a rational function is equal to zero and the numerator is not equal to zero at the same point. We set the denominator equal to zero: $x^2 + 1 = 0$. This equation has no real solutions, so there are no vertical asymptotes.<br /><br />## Step 2: Finding Horizontal Asymptotes<br />### Horizontal asymptotes are determined by examining the limit of the function as $x$ approaches infinity. We evaluate $\lim_{x \to \infty} \frac{x^2 - 1}{x^2 + 1}$. Since the degree of the numerator and denominator are the same, the limit is the ratio of the leading coefficients, which is $\frac{1}{1} = 1$. Thus, there is a horizontal asymptote at $y = 1$.<br /><br />## Step 3: Finding Oblique Asymptotes<br />### Oblique asymptotes occur when the degree of the numerator is exactly one greater than the degree of the denominator. In this case, the degrees are equal, so there are no oblique asymptotes.