Section 2.6 Clicker Problems

1. The graph of $y=x^3$ is shifted 3 units down and 7 units left.
   Which of these is an equation for the new graph?

   A. $y=(x-3)^3-7$
   B. $y=(x-7)^3-3$
   C. $y=(x+7)^3+3$
   D. $y=(x+7)^3-3$
   

   
   
   
   

2. A translation of the graph of $y=x^2$ is shown below. Which of these equations corresponds to the graph?

   A. $y=(x+2)^2-3$
   B. $y=(x-2)^2-3$
   C. $y=(x-3)^2-2$
   D. $y=(x+3)^2-2$
   

   
   
   
   

3. Which of these describes the graph of $y=3+\sqrt[3]{x-4}$ ?

   A. The graph of $y=\sqrt[3]{x}$ shifted down 4 and right 3
   B. The graph of $y=\sqrt[3]{x}$ shifted up 3 and right 4
   C. The graph of $y=\sqrt[3]{x}$ shifted up 3 and left 4
   D. None of the above
   

   
   
   
   

4. The range of $f(x)=x^2$ is $[0,\infty)$. So, what is the range of $g(x)=x^2-5$?

   A. $[5,\infty)$
   B. $[-5,\infty)$
   C. $[0,\infty)$
   D. None of the above