# Honors Algebra 2: Assignment 9: Graphing by Transformations

• Class: Honors Algebra 2
• Author: Peter Atlas
• Text: Algebra and Trigonometry: Structure and Method, Brown

Given the graph of $$y = q(x)$$, describe what the following graphs would look like.
1. $$y = 4q(x)$$
2. Solution The graph of $$q(x)$$ stretched vertically by a factor of 4.
3. $$y = -q(x)$$
4. Solution The graph of $$q(x)$$ flipped upside down.
5. $$\displaystyle y = \frac{1}{5}q(x)$$
6. Solution The graph of $$q(x)$$ squished vertically by a factor of 5.
7. $$\displaystyle y = -\frac{1}{3}q(x)$$
8. Solution The graph of $$q(x)$$ flipped upside down and squished vertically by a factor of 3.
9. $$y = 6q(x - 2)$$
10. Solution The graph of $$q(x)$$ moved to the right 2, and stretched vertically by a factor of 6.
11. $$\displaystyle y = q \left( \frac{x + 1}{3} \right)$$
12. Solution The graph of $$q(x)$$ stretched horizontally by a factor of 3, then moved left by 1.
13. $$\displaystyle y =q \left( \frac{x}{3} + 1 \right)$$
14. Solution The graph of $$q(x)$$ stretched horizontally by a factor of 3, then moved left by 3.
15. $$y = 3q(6x + 2) + 4$$
16. Solution The graph of $$q(x)$$ stretched vertically by a factor of 3, moved up 4, squished horizontally by a factor of 6, moved left by $$\displaystyle \frac{1}{3}$$.
17. $$y = 2 - 3q(8 - x)$$
18. Solution The graph of $$q(x)$$ flipped upside down, stretched vertically by a factor of 3, moved up 2, flipped over the y-axis, moved right by 8.