Which of the following accurately describes the transformation from \( f(x)=\cos (x) \) and \( g(x)=\cos (-x) \) ? Statement \#1: The function \( g(x) \) is a reflection of \( f(x) \) across the \( y \)-axis. Statement \#2: The function \( g(x) \) is a reflection of \( f(x) \) across the \( x \)-axis. Statement \#3: The function \( g(x) \) is a reflection of \( f(x) \) across \( y=x \). (1 point) Statement \# \( \square \) is correct.

What is the general equation of a cosine function with an amplitude of 3 , a period of \( 4 \pi \), and a horizontal shift of \( -\pi \) ? \( \begin{array}{l}y=4 \pi \cos (3(x-\pi)) \\ y=3 \cos (4 \pi(x+\pi)) \\ y=3 \cos (0.5(x+\pi)) \\ y=4 \pi \cos (0.2(x+\pi))\end{array} \)

Starting at its rightmost position, it takes 2 seconds for the pendulum of a grandfather clock to swing a horizontal distance of 18 inches from right to left and 2 seconds for the pendulum to swing back from left to right. Which of the following equations models \( d \), the horizontal distance in inches of the pendulum from the center as a function of time, \( t \), in seconds? Assume that right of center is a positive distance and left of center is a negative distance. \( d=9 \cos \left(\frac{\pi}{4} t\right) \) \( d=9 \cos \left(\frac{\pi}{2} t\right) \) \( d=18 \cos \left(\frac{\pi}{4} t\right) \) \( d=18 \cos \left(\frac{\pi}{2} t\right) \)

Which transformations are needed to change the parent cosine function to \( y=3 \cos (10(x-\pi)) \) ? vertical compression of 3 , horizontal stretch to a period of \( 5 \pi \), phase shift of \( \pi \) units to the left vertical stretch of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the right vertical compression of 3 , horizontal stretch to a period of 10 p, phase shift of \( \pi \) units to the right vertrech of 3 , horizontal compression to a period of \( \frac{\pi}{5} \), phase shift of \( \pi \) units to the left

The equation \( h=7 \sin \left(\frac{\pi}{21} t\right)+28 \) can be used to model the height, \( h \), in feet of the end of one blade of a windmill turning on an axis above the ground as a function of time, \( t \), in seconds. How long is the blade? Assume that the blade is pointing to the right, parallel to the ground, at \( t=0 \), and that the windmill turns counterclockwise at a constant rate. 7 feet 14 feet 21 feet 28 feet

A buoy starts at a height of 0 in relation to sea level and then goes up. Its maximum displacement in either direction is 6 feet, and the time it takes to go from its highest point to its lowest point is 4 seconds. Which of the following equations can be used to model \( h \), the height in feet of the buoy in relation to sea level as a function of time, \( t \), in seconds? \( h=4 \sin \left(\frac{\pi}{6} t\right) \) \( h=4 \sin \left(\frac{\pi}{3} t\right) \) \( h=6 \sin \left(\frac{\pi}{4} t\right) \) \( h=6 \sin \left(\frac{\pi}{2} t\right) \)