find any horizontal or vertical asymptotes. f(x)=1/(x^2 + 1) find the vertical asymptote(s). select the…

find any horizontal or vertical asymptotes. f(x)=1/(x^2 + 1) find the vertical asymptote(s). select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one vertical asymptote, . (type an equation.) b. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is . (type equations.) c. the function has no vertical asymptotes.

find any horizontal or vertical asymptotes. f(x)=1/(x^2 + 1) find the vertical asymptote(s). select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. a. the function has one vertical asymptote, . (type an equation.) b. the function has two vertical asymptotes. the leftmost asymptote is and the rightmost asymptote is . (type equations.) c. the function has no vertical asymptotes.

Answer

Explanation:

Step1: Recall vertical - asymptote condition

Vertical asymptotes occur where the denominator of a rational function is zero. For the function $f(x)=\frac{1}{x^{2}+1}$, set the denominator equal to zero: $x^{2}+1 = 0$.

Step2: Solve the denominator equation

Solve $x^{2}+1 = 0$. Rearrange to get $x^{2}=-1$. In the real - number system, there are no real solutions for $x$ since the square of any real number $x$, $x^{2}\geq0$.

Answer:

C. The function has no vertical asymptotes.