91Ó°ÊÓ

Solve for \(x\) without using a calculating utility. $$ \log _{10}(\sqrt{x})=-1 $$

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=x^{2}, y=\sqrt{x}\), \(y=1 / x, y=|x|,\) or \(y=\sqrt[3]{x}\) appropriately. Then use a graphing utility to confirm that your sketch is correct. $$ y=|x+2|-2 $$

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=x^{2}, y=\sqrt{x}\), \(y=1 / x, y=|x|,\) or \(y=\sqrt[3]{x}\) appropriately. Then use a graphing utility to confirm that your sketch is correct. $$ y=1-|x-3| $$

Find a formula for \(f^{-1}(x),\) and state the domain of the function \(f^{-1}\). $$ f(x)=\sqrt{x+3} $$

Sketch the graph of the equation by making appropriate transformations to the graph of a basic power function. If you have a graphing utility, use it to check your work. $$ \begin{array}{ll}{\text { (a) } y=1-\sqrt{x+2}} & {\text { (b) } y=1-\sqrt[3]{x+2}} \\ {\text { (c) } y=\frac{5}{(1-x)^{3}}} & {\text { (d) } y=\frac{2}{(4+x)^{4}}}\end{array} $$

Solve for \(x\) without using a calculating utility. $$ \ln \left(x^{2}\right)=4 $$

Sketch the graph of the equation by translating, reflecting, compressing, and stretching the graph of \(y=x^{2}, y=\sqrt{x}\), \(y=1 / x, y=|x|,\) or \(y=\sqrt[3]{x}\) appropriately. Then use a graphing utility to confirm that your sketch is correct. $$ y=|2 x-1|+1 $$

Solve for \(x\) without using a calculating utility. $$ \ln (1 / x)=-2 $$

Find a formula for \(f^{-1}(x),\) and state the domain of the function \(f^{-1}\). $$ f(x)=-\sqrt{3-2 x} $$

Use the graph of \(y=\sqrt{x}\) to help sketch the graph of \(y=\sqrt{|x|} .\)