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Magazine Problem 41
\(33-44\) Find the domain and sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}{x+2} & {\text { if } x<0} \\ {1-x} & {\text { if } x \geqslant 0}\end{array}\right.$$
Problem 42
\(33-44\) Find the domain and sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}{3-\frac{1}{2} x} & {\text { if } x \leqslant 2} \\ {2 x-5} & {\text { if } x>2}\end{array}\right.$$
Problem 42
\(41-46 \text { Express the function in the form } \mathrm{f} \circ g.\) $$F(x)=\sin (\sqrt{x})$$
Problem 43
\(41-46 \text { Express the function in the form } \mathrm{f} \circ g.\) $$F(x)=\frac{\sqrt[3]{x}}{1+\sqrt[3]{x}}$$
Problem 43
\(33-44\) Find the domain and sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}{x+2} & {\text { if } x \leqslant-1} \\\ {x^{2}} & {\text { if } x>-1}\end{array}\right.$$
Problem 44
\(41-46 \text { Express the function in the form } \mathrm{f} \circ g.\) $$G(x)=\sqrt[3]{\frac{x}{1+x}}$$
Problem 44
\(33-44\) Find the domain and sketch the graph of the function. $$f(x)=\left\\{\begin{array}{ll}{x+9} & {\text { if } x<-3} \\ {-2 x} & {\text { if }|x| \leqslant 3} \\ {-6} & {\text { if } x>3}\end{array}\right.$$
Problem 44
Compare the functions \(f(x)=x^{0.1}\) and \(g(x)=\ln x\) by graphing both \(f\) and \(g\) in several viewing rectangles. When does the graph of \(f\) finally surpass the graph of \(g ?\)
Problem 45
\(45-50\) Find an expression for the function whose graph is the given curve. $$\begin{array}{l}{\text {The line segment joining the points } (1,-3) and (5,7)}\end{array}$$
Problem 45
\(41-46 \text { Express the function in the form } \mathrm{f} \circ g.\) $$u(t)=\sqrt{\cos t}$$
