Select the correct answer. Which statement describes the vertical asymptote(s), if any, in the graph of the function \( f(x)=\frac{2 x-4}{x^{2}-4} \) ? A. The graph has no vertical asymptotes. B. The graph has one vertical asymptote. C. The graph has two vertical asymptotes. D. The number of asymptotes depends on whether the rational expression is simplified.

To determine the vertical asymptotes of the function \( f(x) = \frac{2x - 4}{x^2 - 4} \), we need to identify the values of \( x \) that make the denominator equal to zero, as vertical asymptotes occur at these points (provided the numerator is not also zero at those points). 1. **Identify the denominator**: The denominator is \( x^2 - 4 \). 2. **Set the denominator to zero**: \[ x^2 - 4 = 0 \] 3. **Solve for \( x \)**: \[ x^2 = 4 \] \[ x = \pm 2 \] Now we have potential vertical asymptotes at \( x = 2 \) and \( x = -2 \). 4. **Check the numerator at these points**: - For \( x = 2 \): \[ 2x - 4 = 2(2) - 4 = 0 \] - For \( x = -2 \): \[ 2(-2) - 4 = -4 - 4 = -8 \neq 0 \] Since the numerator is zero at \( x = 2 \), this means there is a hole in the graph at this point rather than a vertical asymptote. 5. **Conclusion**: The only vertical asymptote is at \( x = -2 \). Thus, the correct answer is: **C. The graph has two vertical asymptotes.**