91Ó°ÊÓ

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. $$f(x)=\frac{x^{3}}{2}-\frac{x^{2}}{2}-2 x+1$$

If \(f(x)=x-1\) and \(g(x)=1 /(x+1),\) find the following. a. \(f(g(1 / 2))\) b. \(g(f(1 / 2))\) c. \(f(g(x))\) d. \(g(f(x))\) e. \(f(f(2))\) f. \(g(g(2))\) g. \(f(f(x))\) h. \(g(g(x))\)

Find the domain and range of each function. $$G(t)=\frac{2}{t^{2}-16}$$

Copy and complete the following table of function values. If the function is undefined at a given angle, enter "UND." Do not use a calculator or tables. $$\begin{array}{llllll} \hline \theta & -3 \pi / 2 & -\pi / 3 & -\pi / 6 & \pi / 4 & 5 \pi / 6 \\ \hline \sin \theta & & & & & \\ \cos \theta & & & & & \\ \tan \theta & & & & & \\ \cot \theta & & & & & \\ \sec \theta & & & & & \\ \csc \theta & & & & & \\ \hline \end{array}$$

Write a formula for \(f \circ g \circ h\). $$f(x)=x+1, \quad g(x)=3 x, \quad h(x)=4-x.$$

one of \(\sin x, \cos x,\) and \(\tan x\) is given. Find the other two if \(x\) lies in the specified interval. $$\sin x=\frac{3}{5}, \quad x \in\left[\frac{\pi}{2}, \pi\right]$$

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. $$f(x)=x^{5}-5 x^{4}+10$$

Write a formula for $f \circ g \circ h$$$f(x)=3 x+4, \quad g(x)=2 x-1, \quad h(x)=x^{2}.$$

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. $$f(x)=4 x^{3}-x^{4}$$

one of \(\sin x, \cos x,\) and \(\tan x\) is given. Find the other two if \(x\) lies in the specified interval. $$\tan x=2, \quad x \in\left[0, \frac{\pi}{2}\right]$$