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. $$y_{1}=x^{3}, \quad y_{2}=x^{3}+4, \quad y_{3}=x^{3}-4$$

Skills Graph each piecewise-defined function in Exercises \(9-20 .\) Is \(f\) continuous on its domain? Do not use a calculator. $$f(x)=\left\\{\begin{array}{ll} 6-x & \text { if } x \leq 3 \\ 3 x-6 & \text { if } x>3 \end{array}\right.$$

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

Write the equation that results in the desired translation. Do not use a calculator. The squaring function, shifted 4 units upward and 1 unit Fo the left

Fill in each blank with the correct response. Do not use a calculator. If a function is even, its graph is symmetric with respect to the _______ If it is odd, its graph is symmetric with respect to the ______.

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

Write the equation 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

Give a short answer to each question. If \(f(a)=-5,\) what is the value of \(|f(a)| ?\)

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

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