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1-7.

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.

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

$y=\frac{2}{3}(x-k)+v$ 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.

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 $-9$.

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.

Refer to the hint in part (d). 