91Ó°ÊÓ

This exercise explores the effect of the inner function \(g\) on a composite function \(y = f ( g ( x ) )\) . (a) Graph the function \(y = \sin ( \sqrt { x } )\) using the viewing rectangle \([ 0,400 ]\) by \([ - 1.5,1.5 ] .\) How does this graph differ from the graph of the sine function? (b) Graph the function \(y = \sin \left( x ^ { 2 } \right)\) using the viewing rectangle \([ - 5,5 ]\) by \([ - 1.5,1.5 ]\) . How does this graph differ from the graph of the sine function?

\(33-44\) Find the domain and sketch the graph of the function. $$F(x)=\frac{1}{2}(x+3)$$

\(33-44\) Find the domain and sketch the graph of the function. $$f(t)=t^{2}-6 t$$

\(33-36\) Find the exact value of each expression. (a) \(\log _{2} 6-\log _{2} 15+\log _{2} 20\) (b) \(\log _{3} 100-\log _{3} 18-\log _{3} 50\)

The figure shows the graphs of \(y = \sin 96 x\) and \(y = \sin 2 x\) as displayed by a TI-83 graphing calculator. The first graph is inaccurate. Explain why the two graphs appear identical. [Hint: The TI-83's graphing window is 95 pixels wide. What specific points does the calculator plot?

\(31-36\) Find the functions (a) \(\mathrm{f} \circ g,(\mathrm{b}) g \circ \mathrm{f},(\mathrm{c}) \mathrm{f} \circ \mathrm{f},\) and \((\mathrm{d}) g \circ g\) and their domains. $$f(x)=x+\frac{1}{x}, g(x)=\frac{x+1}{x+2}$$

\(33-36\) Find the exact value of each expression. (a) \(e^{-2 \ln 5} \quad\) (b) \(\ln \left(\ln e^{e^{*}}\right)\)

\(33-44\) Find the domain and sketch the graph of the function. $$H(t)=\frac{4-t^{2}}{2-t}$$

\(33-44\) Find the domain and sketch the graph of the function. $$g(x)=\sqrt{x-5}$$

\(37-39\) Express the given quantity as a single logarithm. \(\ln 5+5 \ln 3\)