Day 5: Combinations of Transformations REVIEW: Determine the equation of the functions pictured below. FUNCTION 1: 1. List the transformations that need to be applied to 2. Graph to obtain the graph of and state the function’s domain and range. FUNCTION 2: 1. List the transformations that need to be applied to 2. Graph to obtain the graph of . State the period and any points where y = 0. . FUNCTION 3: 1. Graph . State the domain and range. 2. Identify the period and the amplitude. FUNCTION 4: Graph FUNCTION 5: . State the domain and range. Graph . State the range. Independent Practice: 1. Graph . 2. Graph 3. Graph 4. Graph Example #1: . State the domain and range. . . State the equation of the axis, the amplitude and the range. The graph above shows a function y = f(x). Graph the following on the same set of axis: y = 2 f [ -⅔ ( x - 1) + 2 ] Point (-4, -3) (-2, -1) (0, 1) (2, 0) (4, 2) 𝑦 = 𝑎 𝑓 (𝑘 ( 𝑥 − 𝑑)) + 𝑐 a b h k 11. –2 –3 –4 –5 12. 4 2 0 0 13. –1 –1 –1 0 0 –11 horizontal stretch/compression and factor horizontal translation 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 14. 15. 3 H.S. by 4 left 16. –4 0 H.C. by ⅙ 3 right 17. 1 –2 H.S. by 5 none Describe how the graph of each of the following functions can be obtained from the graph of y = f(x). 18. 19. 20. 21. 22. 23. 24. 25. Example #2: a) Graph f(x) = 3 ( x - 2 )2 + 4 Example #3: b) Graph f(x) = 2√−0.25𝑥 Example #4: c) Graph f(x) = − 2 -1 𝑥+5 Example #5: d) Graph f(x) = ⅓ (3 - x - 2 ) - 4 Example #6: e) Graph f(x) = - 4 cos (½ x + 30) + 2 Example #7: f) Determine the equation of the graphs below.