91Ó°ÊÓ

(a) Write formulas for \(f^{\circ} g\) and \(g \circ f\) and find the (b) domain and (c) range of each.$$f(x)=x^{2}, g(x)=1-\sqrt{x}.$$

Find an appropriate graphing software viewing window for the given function and use it to display its graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function. $$y=1-\frac{1}{x+3}$$

Graph the functions.What is the period of each function? $$\cos \left(x-\frac{\pi}{2}\right)$$

Find the natural domain and graph the functions. $$F(t)=t /|t|$$

Graph the functions.What is the period of each function? $$\sin \left(x+\frac{\pi}{6}\right)$$

Find an appropriate graphing software viewing window for the given function and use it to display its graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function. $$f(x)=\frac{x^{2}-1}{x^{2}+1}$$

Find the natural domain and graph the functions. $$G(t)=1 /|t|$$

Graph the functions.What is the period of each function? $$\sin \left(x-\frac{\pi}{4}\right)+1$$

Find the domain of \(y=\frac{x+3}{4-\sqrt{x^{2}-9}}.\)

Find an appropriate graphing software viewing window for the given function and use it to display its graph. The window should give a picture of the overall behavior of the function. There is more than one choice, but incorrect choices can miss important aspects of the function. $$f(x)=\frac{x-1}{x^{2}-x-6}$$