Identify the vertical stretching factor and period of the function. Answer exactly. \( f(x)=-2 \cot (5 x) \) Vertical stretching factor: Period:

For the function \( f(x) = -2 \cot(5x) \): 1. **Vertical Stretching Factor:** The vertical stretching factor is determined by the absolute value of the coefficient multiplying the cotangent function. Here, the coefficient is \(-2\), so the vertical stretching factor is: \[ \text{Vertical stretching factor} = 2 \] 2. **Period:** The period of the cotangent function \( \cot(x) \) is \( \pi \). When the function is of the form \( \cot(Bx) \), the period is adjusted by the factor \( B \). Therefore, for \( \cot(5x) \), the period \( T \) is: \[ T = \frac{\pi}{5} \] **Final Answer:** - **Vertical stretching factor:** \(2\) - **Period:** \(\dfrac{\pi}{5}\)