Graph the function. Give the equations of the vertical and horizontal asymptotes. \( y=\frac{2-\mathrm{x}}{\mathrm{x}-6} \) Give the equations of any vertical asymptotes for the graph of the rational function. Select the correct choice and, if necessary, fil in the answer box(es) within your choice. A. The function has one vertical asymptote. The vertical asymptote is (Simplify your answer. Type an equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \( \square \) and the rightmost asymptote is (Simplify your answers. Type equations.)

To find the vertical asymptotes of the function \( y=\frac{2-x}{x-6} \), you need to identify where the denominator equals zero since these are the points where the function is undefined. Setting \( x - 6 = 0 \) gives us \( x = 6 \). Therefore, the function has one vertical asymptote at \( x = 6 \). Now, for horizontal asymptotes, we analyze the degrees of the polynomial in the numerator and denominator. Since they are both linear (degree 1), we look at the leading coefficients. The horizontal asymptote is given by \( y = \frac{2}{1} = 2 \). So for the selections: A. The function has one vertical asymptote. The vertical asymptote is \( x=6 \). Additionally, keep in mind that functions like this can often present interesting behaviors! Like how vertical asymptotes create boundaries that the graph dances around, giving rise to amusing shapes and moments. Understanding these asymptotes can also help you predict the behavior of the function as \( x \) approaches those critical values. If you're plotting the graph, you might notice the graph will move towards the asymptotes but never actually touch them—making them significant guiding lines in your analysis!