91Ó°ÊÓ

In Exercises \(57-66,\) state the domain and range of the functions. $$y=2-\csc \left(\frac{1}{2} x-\pi\right)$$

In Exercises \(61-66,\) sketch the graph of the function over the indicated interval. $$y=\frac{1}{3}+\frac{2}{3} \sin (2 x-\pi),\left[-\frac{3 \pi}{2}, \frac{3 \pi}{2}\right]$$

In Exercises \(57-66,\) state the domain and range of the functions. $$y=1-2 \sec \left(\frac{1}{2} x+\pi\right)$$

In Exercises \(57-66,\) state the domain and range of the functions. $$y=-3 \tan \left(\frac{\pi}{4} x-\pi\right)+1$$

Refer to the following: The height of the water in a harbor changes with the tides. The height of the water at a particular hour during the day can be determined by the formula \(h(x)=5+4.8 \sin \left[\frac{\pi}{6}(x+4)\right]\) where \(x\) is the number of hours since midnight and \(h\) is the height of the tide in feet. The average number of guests visiting the Magic Kingdom at Walt Disney World per day is given by \(n(x)=30,000+20,000 \sin \left[\frac{\pi}{2}(x+1)\right],\) where \(n\) is the number of guests and \(x\) is the month. If January corresponds to \(x=1\) how many people on average are visiting the Magic Kingdom per day in February?

In Exercises \(61-66,\) sketch the graph of the function over the indicated interval. $$y=\frac{1}{2}-\frac{1}{2} \sin \left(\frac{1}{2} x-\frac{\pi}{4}\right),\left[-\frac{7 \pi}{2}, \frac{9 \pi}{2}\right]$$

In Exercises \(57-66,\) state the domain and range of the functions. $$y=\frac{1}{4} \cot \left(2 \pi x+\frac{\pi}{3}\right)-3$$

In Exercises \(61-66,\) sketch the graph of the function over the indicated interval. $$y=-\frac{1}{2}+\frac{1}{2} \cos \left(\frac{1}{2} x+\frac{\pi}{4}\right),\left[-\frac{9 \pi}{2}, \frac{7 \pi}{2}\right]$$

In Exercises \(57-66,\) state the domain and range of the functions. $$y=-2+\frac{1}{2} \sec \left(\pi x+\frac{\pi}{2}\right)$$

In Exercises \(61-66,\) sketch the graph of the function over the indicated interval. $$y=-3+4 \sin [\pi(x-2)],[0,4]$$