91Ó°ÊÓ

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=x^{2}, \quad y_{2}=(x-2)^{2}+1, \quad y_{3}=-(x+2)^{2}$$

Give a short answer to each question. Why can't the range of \(y=|f(x)|\) include \(-1,\) for any function \(f ?\)

Explain how the graph of \(g(x)=f(x+4)\) is obtained from the graph of \(y=f(x)\).

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} x^{3}+5 & \text { if } x \leq 0 \\ -x^{2} & \text { if } x>0 \end{array}\right.$$

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$\left(\frac{f}{g}\right)(4)$$

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f-g)(2)$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 2 x & \text { if }-5 \leq x<-1 \\ -2 & \text { if }-1 \leq x<0 \\ x^{2}-2 & \text { if } 0 \leq x \leq 2 \end{array}\right.$$

Use graphing to determine the domain and range of \(y=f(x)\) and of \(y=|f(x)|\). $$f(x)=(x+1)^{2}-2$$

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=|x|, \quad y_{2}=-2|x-1|+1, \quad y_{3}=-\frac{1}{2}|x|-4$$

Use transformations of graphs to sketch the graphs of \(y_{1}, y_{2},\) and \(y_{3}\) by hand. Check by graphing in an appropriate viewing window of your calculator. $$y_{1}=\sqrt{x}, \quad y_{2}=-\sqrt{x}, \quad y_{3}=\sqrt{-x}$$