\( \mathrm{R}(\mathrm{x})=\frac{7 \mathrm{x}}{\mathrm{x}+7} \) Find the vertical asymptotes. 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. Use integers or fractions for any numbers in the equation.) B. The function has two vertical asymptotes. The leftmost asymptote is \( \square \) and the rightmost asymptote is \( \square \). (Type equations. Use integers or fractions for any numbers in the equations.) C. The function has no vertical asymptote.

To find the vertical asymptotes of the function \( R(x) = \frac{7x}{x + 7} \), we need to determine where the function is undefined. Vertical asymptotes occur at values of \( x \) that make the denominator equal to zero, provided that the numerator is not also zero at those points. 1. **Identify the denominator**: The denominator of the function is \( x + 7 \). 2. **Set the denominator equal to zero**: \[ x + 7 = 0 \] 3. **Solve for \( x \)**: \[ x = -7 \] Now, we check the numerator at this point: - The numerator \( 7x \) at \( x = -7 \) is \( 7(-7) = -49 \), which is not zero. Since the denominator is zero and the numerator is not zero at \( x = -7 \), there is a vertical asymptote at this point. Thus, the function has one vertical asymptote. The correct choice is: **A. The function has one vertical asymptote,** \[ x = -7 \]