TRANSLATING FUNCTIONS  

1. Graph the function $y = \frac { 2 } { 3 } x ^ { 2 }$. On the same set of axes graph a translation of the function that is shifted one unit to the right and five units down. Write the equation of the translated function.

   Answer (a):

   $y=\frac{2}{3}(x-1)^2-5$
   

2. Does the same strategy work for $y = \frac { 2 } { 3 } x$? Write an equation that will shift $y = \frac { 2 } { 3 } x$ one unit to the right and five units down.

   Answer (b):

   $y=\frac{2}{3}(x-k)+v$ What are $k$ and $v$? 

3. Compare the graphs of and $y = - \frac { 1 } { 2 } x$ and $y = - \frac { 1 } { 2 } ( x + 2 ) + 3$. Describe their similarities and differences.

   Hint (c):

   Both graphs are straight lines with the same slope. The second graph has been shifted both horizontally and vertically.

4. Explain how you know that the graph of $y = -9(x + 1) - 6$ goes through the point $(-1, -6)$ and has a slope of $-9$.

   Hint (d):

   This is a straight line in Point-Slope form. See Math Note for more information.
   

5. Sketch the graph of $y = 5(x - 2) - 1$ quickly.

   Hint (e):

   Refer to the hint in part (d).