### Home > APCALC > Chapter 1 > Lesson 1.1.1 > Problem1-7

1-7.

TRANSLATING FUNCTIONS Homework Help ✎

1. Graph the function y = $\frac { 2 } { 3 }$x2. On the same set of axes graph a translation of the function that is shifted 1 unit to the right and 5 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 1 unit to the right and 5 units down.

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

3. Compare the graphs of 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 from

$y = -\frac{1}{2}x.$

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.

Refer to the hint in part (d).