91Ó°ÊÓ

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The square root function, shifted 3 units upward and 6 units to the left

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

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

Give a short answer to each question. How does the graph of \(f(x)=x^{2}\) compare with the graph of \(f(x)=\left|x^{2}\right| ?\)

Let \(f(x)=x^{2}+3 x\) and \(g(x)=2 x-1 .\) Perform the composition or operation indicated. $$(f+g)(-5)$$

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The absolute value function, shifted 1 unit downward and 5 units to the right

Write an equation in \(x\) and \(y\) that results in the desired translation. Do not use a calculator. The squaring function, shifted 2000 units to the right and 500 units upward

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

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. $$y_{1}=\sqrt{x}, \quad y_{2}=\sqrt{x+6}, \quad y_{3}=\sqrt{x-6}$$

Graph each piece wise-defined function. Is \(f\) continuous on its entire domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 2+x & \text { if } x<-4 \\ -x & \text { if }-4 \leq x \leq 5 \\ 3 x & \text { if } x>5 \end{array}\right.$$