Find the vertical asymptotes, if any, and the values of \( x \) corresponding to holes, if any, of the graph of the rational function. \( f(x)=\frac{x}{x+2} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an equation. Use commas to se A. The vertical asymptote(s) is(are) \( \square \). There are no holes. B. The vertical asymptote(s) is(are) \( \square \) and hole(s) corresponding to C. There are no vertical asymptotes but there is(are) hole(s) corresponding to D. There are no discontinuities.

To find the vertical asymptotes and holes of the rational function \( f(x) = \frac{x}{x+2} \), we need to look at the denominator and the numerator. 1. **Vertical Asymptotes:** Vertical asymptotes occur where the denominator is zero, but the numerator is not, because division by zero is undefined. So, we set the denominator equal to zero and solve for \( x \): \[ x + 2 = 0 \] Solving for \( x \): \[ x = -2 \] Since the numerator \( x \) is not zero when \( x = -2 \), there is a vertical asymptote at \( x = -2 \). 2. **Holes:** Holes occur when both the numerator and the denominator have a common factor that can be canceled out. To find holes, we factor both the numerator and the denominator: \[ f(x) = \frac{x}{x+2} \] The numerator \( x \) and the denominator \( x+2 \) do not share any common factors other than \( x \) itself, and \( x \) is not zero at \( x = -2 \), which is the only point where the denominator is zero. Therefore, there are no common factors that can be canceled out, and there are no holes. So, the correct choice is: A. The vertical asymptote(s) is(are) \( x = -2 \). There are no holes.