91Ó°ÊÓ

Write the equation that results in the desired translation. Do not use a calculator. The squaring function, shifted 1000 units to the left and 255 units downward

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. $$y_{1}=|x|, \quad y_{2}=2|x|, \quad y_{3}=2.5|x|$$

Skills Graph each piecewise-defined function in Exercises \(9-20 .\) Is \(f\) continuous on its domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} -2 x & \text { if } x<-3 \\ 3 x-1 & \text { if }-3 \leq x \leq 2 \\ -4 x & \text { if } x>2 \end{array}\right.$$

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

Skills Graph each piecewise-defined function in Exercises \(9-20 .\) Is \(f\) continuous on its domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} -\frac{1}{2} x^{2}+2 & \text { if } x \leq 2 \\\ \frac{1}{2} x & \text { if } x>2 \end{array}\right.$$

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. $$y_{1}=\sqrt[3]{x}, \quad y_{2}=-\sqrt[3]{x}, \quad y_{3}=-2 \sqrt[3]{x}$$

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

Give a short answer to each question. If the range of \(y=f(x)\) is \((-\infty,-2],\) what is the range of \(y=|f(x)| ?\)

Write the equation that results in the desired translation. Do not use a calculator. Explain how the graph of \(g(x)=f(x)+4\) is obtained from the graph of \(y=f(x)\)

Write the equation that results in the desired translation. Do not use a calculator. Explain how the graph of \(g(x)=f(x+4)\) is obtained from the graph of \(y=f(x)\)