Questions: Determine the period of the function (y=cos left(-frac14 xright)) and sketch its graph. Choose the correct graph of (y=cos left(-frac14 xright)) below. A. B. C. D.

Solution Steps

The given function is \( y = \cos\left(-\frac{1}{4}x\right) \). This is a cosine function with a horizontal scaling factor.

The standard period of the cosine function \( y = \cos(x) \) is \( 2\pi \). For a function of the form \( y = \cos(bx) \), the period is given by \( \frac{2\pi}{|b|} \).

Here, \( b = -\frac{1}{4} \). Therefore, the period \( T \) is: \[ T = \frac{2\pi}{\left| -\frac{1}{4} \right|} = \frac{2\pi}{\frac{1}{4}} = 8\pi \]

The correct graph should have a period of \( 8\pi \). Among the given options, the graph that shows a complete cycle from \( 0 \) to \( 8\pi \) is the correct one.

Final Answer