What are the transformations of the graph of the function \( f(x)=\frac{1}{x} \) when it is replaced by \( k(x)=-\frac{4}{7 x} \) ? (1 point) It reflects across the \( y \)-axis and vertically stretches by a factor of \( \frac{7}{4} \). It reflects across the \( x \)-axis and vertically stretches by a factor of \( \frac{7}{4} \). It reflects across the \( x \)-axis and vertically compresses by a factor of \( \frac{4}{7} \). It compresses by a factor of \( \frac{4}{7} \).

To determine the transformations from \( f(x) = \frac{1}{x} \) to \( k(x) = -\frac{4}{7x} \), we notice that the negative sign indicates a reflection across the \( x \)-axis. Furthermore, the coefficient \(-\frac{4}{7}\) shows that the function is also vertically stretched by a factor of \( \frac{4}{7} \) (since we are actually looking at the absolute value of the stretch factor). In total, there is a reflection across the \( x \)-axis and a vertical compression (not stretching) by a factor of \( \frac{4}{7} \). Thus, the correct answer is: It reflects across the \( x \)-axis and vertically compresses by a factor of \( \frac{4}{7} \).