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.)

**A.** The function has one vertical asymptote. The vertical asymptote is \[ x = 6 \] --- **Explanation:** To determine the vertical asymptotes of the rational function \( y = \frac{2 - x}{x - 6} \), follow these steps: 1. **Identify the Denominator:** The vertical asymptotes occur where the denominator is zero (since the function is undefined there). 2. **Set Denominator Equal to Zero:** \[ x - 6 = 0 \] \[ x = 6 \] 3. **Conclusion:** There is only one value of \( x \) that makes the denominator zero, which is \( x = 6 \). Therefore, the function has a single vertical asymptote at \( x = 6 \). --- **Additional Information:** - **Horizontal Asymptote:** For completeness, if you're also interested in the horizontal asymptote of the function: \[ y = \frac{2 - x}{x - 6} = \frac{-x + 2}{x - 6} \] The degrees of the numerator and denominator are both 1. The horizontal asymptote is determined by the ratio of the leading coefficients: \[ y = \frac{-1}{1} = -1 \] So, the horizontal asymptote is \( y = -1 \). - **Graphing the Function:** When graphing the function, you'll see that as \( x \) approaches 6 from either side, the function values will grow without bound (either positively or negatively), illustrating the vertical asymptote at \( x = 6 \). The function will approach \( y = -1 \) as \( x \) moves towards positive or negative infinity.